They had their differences. He was into restoration; she preferred new. She wanted to keep the original façade and floors, he wanted to redo them. He won that battle.

But Ms. Greenspon has won others. The two are business partners, not romantic partners, and Algus Greenspon, their West Village art gallery, has the smooth cement floors he wanted but also shows some of the young artists she prefers.

Even by art world standards, it is a peculiar arrangement. What has made it work?

The two first spoke around 2000, when Ms. Greenspon was at NYU and working for the PaceWildenstein gallery. She contacted Mr. Algus because she was interested in buying a painting by the obscure Pop artist Nicholas Krushenick, whom he had shown. “I remember calling, and someone answered,” she said. “They were like, ‘Mitchell doesn’t come in until after 4.’ I thought, ‘O.K.. This guy must be really important.’”

A lot of people—high-profile artists, curators and writers—really do hold Mr. Algus in high regard. But the real reason he wasn’t at the gallery was that he was at Long Island City High School.

Mr. Krushenick was not the only obscure artist Mr. Algus showed. There were also Larry Zox, Harold Stevenson, Rosalyn Drexler and dozens more. From 1992 until he joined with Ms. Greenspon, he specialized almost exclusively in the work of unknown or forgotten artists from the 1960s and ’70s. He was heralded for reviving careers, sometimes to his own detriment.

“It’s the ones like Lee Lozano who get upsetting because you realize how powerless you are,” he said on a recent late afternoon over iced coffees at the Eli’s Essentials café next to the Whitney Museum. He’d just finished teaching. One of the leading conceptual artists in New York in the 1960’s, Ms. Lozano quit the art world and was virtually unknown when he and other dealers presented her work in 1998, shortly before her death. Museum retrospectives followed those shows, and international powerhouse Hauser & Wirth now works with her estate.

“We were trying to sell a painting for $18,000 that would go for over a million now,” he said. “Money is sexy. A painting that is a million dollars is a lot more sexy than a painting that is $18,000. It’s very frustrating. You realize that is the way the art world is.”

An article in this month’s Forbes discusses today’s high-flying art market and talks about dealers being celebrities. Most aren’t.

“The art market,” Mr. Algus said at Eli’s, “has never meant anything to me.” Dealers often say this, but in Mr. Algus’s case it appears to be true. Over two decades he has run four relatively quiet galleries in four different neighborhoods, while by his own admission selling very little.

Selling was not really the point. It was about getting under people’s skin, aesthetically speaking. “I really dislike consensus,” he said. He propped his glasses on his head and continued emphatically, “When everybody agrees on something I just feel like it’s all the nasty kids I hated in high school, and so, if things can undermine consensus, that’s sort of what I’m interested in.”

That would be South Side Senior High School, in Rockville Centre on Long Island. “He had these swept bangs,” recalled artist Deborah Kass, a fellow student. “He was fucking adorable.” Mr. Algus is pretty much bald today, but still radiates boyish enthusiasm. At Eli’s, The Observer admitted unfamiliarity with the painter Louis Eilshemius. “You don’t know Louis Eilshemius?” He gaped in horror, then pulled up JPEGS on his laptop.

Art wasn’t originally in the cards for Mr. Algus. Though his father bought art magazines and took him to galleries, he studied geology at Harpur College, now SUNY Binghampton, and got his master’s in the subject at McGill University in Montreal. “I really wanted to go up to the Canadian Arctic. That whole British ‘to the ends of the Earth’ tradition was really alive there.”

He went to the University of Colorado-Boulder to get his doctorate and found himself hanging out in the art history department. But, he said, “It was very pretentious. It was really intellectually rigorous and very dry.” He went back to McGill and got his Ph.D. in geology.

In 1986, he moved back to New York to teach grad school, and he and a friend opened a gallery in Williamsburg. He was also making art—small assemblages he exhibited at East Village galleries.

Williamsburg was uncharted territory. “We would have an opening and there would be 500 people out in the street,” Mr. Algus said. They showed their friends’ work. “We would have a bonfire, and then no one would come again. It was just a party, and then a month of nothing.”

One day Mr. Algus’s girlfriend, Dyanne (who is now his wife), had her wallet stolen from her car. A man who’d done odd jobs for the gallery learned the thieves wanted $40 for it. “Then I get a phone call that he got into a fight with somebody and stabbed him and he needed a plane ticket to Puerto Rico and he was living in the basement hiding out from the police. So, the gallery was over.”

His next gallery, which he opened about nine months later, in November 1992, was on Thompson Street in Soho. There he began dusting off artists he’d read about in his father’s old art magazines. He stopped teaching graduate school and moved to a high school so that he could head to the gallery in the late afternoon.

He opened with The New Adam, a 39-foot-long nude portrait of Sal Mineo that painter Harold Stevenson—a well-regarded but then-unknown artist—made in 1962. The painting, which was subsequently donated to the Guggenheim, took up his whole gallery.

“He was like a fairy godmother for us,” Betty Tompkins said in her Soho loft recently, surrounded by a few of her “Fuck Paintings”—huge, virtuosic black-and-white airbrushed canvases of heterosexual penetration—that Mr. Algus showed, ending a decades-long drought in her career, which subsequently took off. Her first “Fuck Painting,” from 1969, is now owned by Paris’s Centre Pompidou.

Unlike at many galleries, women were integral to Mr. Algus’s program. There were Ms. Lozano and Ms. Tompkins, but also Joan Semmel, who paints fleshy full-body portraits, often in lurid colors, and Judith Bernstein, who’s known for brawny drawings of flying penises that sometimes cover entire walls.

All of those artists were mid-career or well past it when Mr. Algus entered the picture, and all now work with other galleries. When his artists moved on, they generally did so with Mr. Algus’s blessing. “It’s good, because I don’t want to represent people in that way,” he said. “It takes the pressure off me.”

With a small space, low overheard and few employees, he could be discerning in how he operated. “I was actually there at the gallery one time, and he’s on the phone with somebody—a collector, I think,” Ms. Tompkins said. She recalled him saying firmly, “No, that’s not what I do. I teach school so I can have the privilege of saying no to things like this.’”

After working at Pace, Ms. Greenspon became an art advisor and then worked for dealer Marianne Boesky, where she organized a Krushenick show after Mr. Algus put her in touch with his widow. Her father, William Greenspon, whose extensive art and Bauhaus furniture collection has been profiled in The New York Times, had impressed on her a mission similar to Mr. Algus’s. “‘There are these opportunities, Amy, you should be looking for,’” she said he told her of the underrated Krushenick.

Mr. Algus’s gallery, which he moved to a small second-floor space in Chelsea in 2002, was also an inspiration for her. “I would go over and see his shows and sit down and talk. It was a refreshing and interesting place, a very special environment. Artists were always coming in and out.” She proposed a partnership.

“I had been doing it for so long by myself, it sounded like something that was worth trying,” Mr. Algus explained. “It’s easy for me to do shows, and it’s better if I don’t have to deal with all the other stuff.” Plus he has a lot more space.

Mr. Algus and Ms. Greenspon have had what’s referred to in couple’s therapy as constructive arguments. “Sometimes he would show me things, and I would be like, ‘My God, that is the most hideous thing,’” said Ms. Greenspon. “Then I would think, ‘He’s right. This artist is up to something interesting.’ The same goes in the other direction. Artists of my generation who I found to be really intelligent, if it didn’t look like it was made by a 75-year-old man or woman, it wasn’t really his vibe, but he also comes around.”

She began representing her artist friends Emily Sundblad, Adriana Lara and Mathew Cerletty, who helped design the space. “Because it is much more professional, suddenly artists saw it as something hot,” said Adrian Dannatt, an art journalist and friend of Mr. Algus.

“A more effective way for a gallery to make money is to chase trends,” said Mr. Cerletty, a painter who dated Ms. Greenspon for two years. “But I think it appealed to artists that the gallery’s program has integrity.” Mr. Algus’s gallery always had integrity, but his new place also has buzz.

The two partners don’t always agree about whom to show. “The most difficult thing right now is not having the freedom to be nice to people,” Mr. Algus said. Before, he could show an obscure artist on a whim. “Before, I could be nice to everybody.” Said Ms. Greenspon, “The space demands a certain level of quality and reverence.”

The new space was pricey. “We don’t have a backer,” Ms. Greenspon said. “It was outrageously expensive and it was money we had saved over the years.” As she watched that new floor go in, she said she thought, “How many Murakamis did I have to sell for this?”

At Eli’s, Mr. Algus made the partnership sound not exactly harmonious. “Wait, he went there?” Ms. Greenspon said incredulously, on the phone. “It’s not, for us personally,” she said. “But for the good of the gallery it’s pretty genius—our complementary, sometimes antagonistic approaches. We hadn’t curated or done anything together like that before, and if we had, maybe we wouldn’t have opened the gallery, but I’m glad we didn’t, because it’s forced us to work together and compromise.”

She said she didn’t expect him to be such a “spendthrift.” She was half joking. He started calling himself “the adult” before cutting himself off. But while he’s pained about not showing some of his funkier oldies, he seems to get a kick out of her younger artists. She can now admit that her idea to inaugurate the gallery with a Balthus retrospective was “totally naïve”; then again, she’s been busy selling sculptures from their current show of Algus favorite Bill Bollinger to, she bubbled to The Observer, “really good places.” They seem to find each other amusing.

But can such an unusual alliance endure?

“They definitely butt heads and have fights,” Mr. Cerletty said. “It seems like the gallery is going to close every time there is a show, but it usually works out, and everyone thinks it looks better for having fought it out.”

When we asked Mr. Algus about selling, he looked uncomfortable. “I hate telling people what to think,” he said. “The shows do it. I’ve listened to very well-known dealers do it, and it gives me the creeps. It makes my skin crawl. Why should I have to sell this to you?”

arusseth@observer.com

Installation view of Danh Vo's "Autoerotic Asphyxiation" exhibition at Artists Space, 2010. (Photo by Daniel Pérez, courtesy of Artists Space)

When Stefan Kalmár arrived at the alternative art space Artists Space in the summer of 2009 to become its executive director, he saw plenty of things that he wanted to change.

“The director’s office was a corner office with a vista,” Mr. Kalmár said earlier this month, with a touch of mockery, “symbolizing a petit-bourgeois notion of an institution. There was a real hierarchy.” The robust 41-year-old was wearing a tight sweater, torn near the elbows, over a collared shirt, and was sitting in Artists Space’s third-floor loft on Greene Street, pointing to where various rooms had been. “Next to me was the assistant to the director’s office, and then there was the development office. Like chicken hatches. In this corner was the boardroom, and here was storage and a facility room, and an archive. Everything that an organization doesn’t—shouldn’t—need.”

He had walls torn down, floors sanded. Now, light streams into the exhibition space, and the staff members--there are four full-time employees and four part-timers--work in a cluster of desks in a corner.

He shipped the archive off to NYU’s Fales Library.

“If an organization gets busy with its own history,” he said, “it’s kind of fucked.”

Instead, he’s thinking about its future. Next month, Artists Space opens a 2,500-square-foot satellite location at nearby 55 Walker Street, which will host talks and other public events, small exhibitions and a modest bookstore. If all goes according to plan, there will be a cinema of the same size in the basement by the end of the year.

For a small organization that has sometimes struggled to attract attention—even to stay in operation—the plans are ambitious, and they come at a time when the very definition of the so-called alternative space is undergoing dramatic revision.

> Click to see images from Artists Space exhibitions.

Today’s art world is quite a bit different from the one in which Artists Space was founded, in 1972, by Irving Sandler and Trudie Grace, as a nonprofit gallery where emerging artists could show work at a time when, comparatively speaking, there was barely a market for contemporary art.

“There were a lot of old, abandoned or nearly empty, funky office buildings downtown, which had these smoky glass doors that were straight out of Sam Spade’s office in The Maltese Falcon,” recalled art adviser Allan Schwartzman, who was recently named president of Artists Space’s board, along with artist Rachel Harrison. Real estate was cheap then, and artists and curators took up residence.

“In the early 1970s, you had maybe 70 galleries,” Mr. Kalmár said. “But now you have 700 galleries.” In 1973, the year Artists Space opened above the Paula Cooper Gallery on Wooster Street, Sotheby’s held its first major contemporary art auction. The coincidence is weirdly prophetic: These days, nothing sells like new art, with contemporary art fairs proliferating and Christie’s reporting that the category was its largest revenue generator last year.

As the curator Anthony Huberman, who runs a Lower East Side alternative space in conjunction with Hunter College called the Artist’s Institute, noted, major museums, as well as commercial galleries like Reena Spaulings and Alex Zachary Peter Currie, are showing much of today’s most venturesome art. Not only is young art selling, but some of the most radical art is finding willing buyers. “[T]he role historically played by alternative spaces has been made somewhat redundant,” Mr. Huberman has written.

“Alternative space came to mean a particular kind of organizational structure that is now outdated,” said Mary Ceruti, executive director of Long Island City's SculptureCenter. “I think the other term that is more descriptive and has been able to evolve is ‘artist-run’ space, which is now perhaps ‘artist-centered.’”

So how do alternative spaces evolve to stay relevant, and funded? And what’s their point?

New York’s longtime spaces have undergone major transitions over the past two decades. Many have shuttered, like the Bronx’s Fashion Moda, Thread Waxing Space (founder Tim Nye is now a commercial dealer) and the 30-year-old Exit Art, which will close its doors next month, following the death last year of cofounder Jeanette Ingberman. Others, such as the Alternative Museum and Franklin Furnace, have transitioned into online organizations.

Still others have grown steadily more institutional, like PS1 in Queens, which became an affiliate of the Museum of Modern Art in 2000, after years of financial struggles, and the New Museum, which began in 1977 in a small office in an upper floor of 105 Hudson Street, called the Fine Arts Building at the time, and moved in 2007 into a gleaming, seven-story, $50 million structure on the Bowery designed by SANAA. (The ground floor of 105 Hudson is now an outpost of the Asian-fusion restaurant Nobu.)

Artists Space’s trajectory has been more peculiar. Back in 1977, it was in the same Fine Arts Building, directed by curator Helene Winer, who now co-owns the Chelsea gallery Metro Pictures. “It was the most important exhibition space for contemporary art in New York City,” said Mr. Schwartzman, who helped start the New Museum.

That same year, Artists Space hosted the seminal “Pictures” show, introducing era-defining artists like Robert Longo and Sherrie Levine. In following years it developed a reputation for being willing to court controversy, showing institutional critique work and art related to gay rights and AIDS activism, by artists like Nan Goldin and David Wojnarowicz, whose catalogue essay for one show in the late ’80s led to grant money being revoked.

“The history of Artists Space mirrors the arc of what a critical art institution is thought to be at various times,” Artists Space curator Richard Birkett said. Throughout, it has had a left-wing edge, providing space for groups like Artists Meeting for Social Change and AIDS activists.

But New York’s alternative spaces have life cycles. Their statuses fluctuate with the times. Some curatorial programs click, others fall flat. By the mid-2000s, many say, Artists Space was well into a slump. One dealer told The Observer, “Its program was completely irrelevant.”

Until joining Artists Space, Mr. Kalmár had been directing the Kunstverein Munich—a municipal contemporary art museum. A few years ago, he was having a drink with British artist Liam Gillick, who had moved to New York in the ’90s and whom Mr. Kalmár had worked with on a project. Mr. Gillick, a longtime Artists Space board member, asked him for advice about hiring a new director. Did he have any suggestions?

“It took just one more drink,” Mr. Kalmár said. “And I was like, ‘Yeah … me!’ He wasn’t asking or thinking of me, because he was thinking, ‘Why would you leave a very well-funded institution in Munich?’

“When I took the job in Munich, I always said, ‘Look, if I’m turning 40 in Munich, something went wrong, and you should fire me, as it would mean I have become complacent. Munich is a very, very comfortable city.’”

“Stefan had that thing I used to have when I first came to New York,” Mr. Gillick told The Observer, “which is that New York has potential. I think the board got this intense feeling that he was coming with the idea that the place, that the city, has potential.”

These days, few doubt Mr. Kalmár’s ambition. “Stefan is plugged into what a lot of younger curators are interested in,” said the gallerist Mitchell Algus, who has worked with him.

Many of the artists Messrs. Kalmár and Birkett have elected to show are not emerging ones, but rather older, often-obscure figures whom larger institutions have ignored, like Charlotte Posenenske, who made mutable sculptures in the 1960s before quitting the art world to become a sociologist, and Mark Morrisroe, a photographer of downtown New York’s gay communities in the ’80s.

“People still saw Artists Space as a sort of advocacy organization that should promote young artists’ careers,” Mr. Kalmár said, “that we should essentially test run artists for the market, and I don’t think that’s what we should do. Our thing is to make a program.

“Unlike any other organization, we are the space for artists,” he said. “But we are not necessarily the space for artists by showing them.” Instead, it means providing a discursive space for artists (hence the 55 Walker branch) and meeting with a group calling itself Working Artists and the Greater Economy, which advocates that artists be paid fees when producing work for institutions.

In October, Mr. Kalmár also inadvertently hosted an event with a group inspired by the Occupy Wall Street movement, which took up residence in the building. The group, which included artists, held sometimes tense discussions with the staff and refused to speak with press. Staff claim that an occupier broke into a storage locker and removed a laptop. After about 28 hours, the board voted to ask them to leave, and, in the presence of security guards, they complied.

“The language used, the aggression used, didn’t make me believe that this was a utopian, more democratic moment.” Mr. Kalmár said, quickly adding, “I think for all parties this was an interesting experience.”

“I think it tells you something about Stefan,” Mr. Gillick said of the incident. “He would neither be the hip dad with the kids, sitting down and barricading himself in with them and hanging the banner outside to look good, but he also wouldn’t be the asshole either.

“He asked questions and tried to confront the situation but also be flexible and move with it. As we get further away from that event, you can see it as a kind of marker of something. It set a kind of line in the sand, and we’re not sure where it is. The thing’s not over.”

For the moment, things are looking up for Artists Space. Reviews have been largely favorable. The second location is set to open. The curators are at work on exhibitions with critical favorites the Bernadette Corporation and Chris Kraus. Revenue for fiscal year 2010-11 was up 35 percent over the previous year, according to Mr. Kalmár, mostly thanks to increased individual giving.

“We can’t offer them canapé-and-Champagne receptions,” Mr. Kalmár said of his donors. “What we can do is make them proud of being involved in something that contributes to the artists living and working in New York, and continues to generate discussion among them.”

“I have always believed that vision sells,” he continued. And he added later, “Pie charts and visitor profiles—this, in the long run, will cause disaster for the organization. Integrity and a vision are the only things we have, not much else.”

In an art world as large as today’s, and one so dominated by the market, that may be the key to successful alternative spaces’ appeal.

The board has attracted high-powered market types like Mr. Schwartzman, dealer Lawrence Luhring and Frieze Art Fair director Amanda Sharp, as well as prominent artists like Rirkrit Tiravanija and Ms. Harrison, and they’re all working to build an organization with an annual budget of only about $1 million—less than the price of many Damien Hirst spot paintings—into a place that can host important debates, and maybe provoke some arguments.

“We have always had a sort of a joke here,” Mr. Kalmár said. “Initially I wanted to use this as a slogan, but I was stopped from doing that.” A few staff members looked over from their computers with nervous smiles. “It was, ‘Forty years and still old school.’”

arusseth@observer.com

Correction: An earlier version of this piece incorrectly stated that Roland Augustine is a member of Artists Space's board. Lawrence Luhring, however, is. In addition, we have clarified that the Wojnarowicz controversy led to the cancellation of grant money.