The critics were in awe: Rene Magritte, Willem de Kooning, Andy Warhol, Roy Lichtenstein, Max Ernst, Jasper Johns, Max Weber - extraordinary works of contemporary art, all put on exhibition this month in the same unlikely place - a small museum on the campus of Brandeis University near Boston.

The show was "astounding", wrote the reviewer for The Boston Globe. Even in art-rich Boston, he observed, no other museum could provide a "comparable sense of the excitement engendered by European and, especially, American modernism".

Still more astounding is this: Brandeis' Rose Art Museum may soon be no more. The university's board of trustees this year voted unanimously to sell the whole collection, saying they need the money in a time of stretched resources. And while the decision was deferred in the face of public outrage and the university's embattled president retired, Brandeis has reserved the right to sell the art.

It's one of several such instances in which cash-strapped American universities have sold, or threatened to sell, works of art and other parts of their collections, and even whole museums, in controversies that have awakened public attention to university cultural holdings and pushed museum directors to make the institutions more relevant to the academic curriculum.

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"Nobody likes a crisis, but what is it they say? A crisis is a terrible thing to waste," says David Alan Robertson, president of the Association of College and University Museums and Galleries. He argues that there has not been such a grave threat to the sector's museums since Yale University opened the first such institution in 1831 with a gift from the London-trained artist John Trumbull.

There are 770 accredited university museums in the US, and 15 per cent of American museums are on university campuses.

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"It all has to do with economics," contends Robertson, who is director of the Mary and Leigh Block Museum of Art at Northwestern University. "Art accrues in value. You can divest of scientific equipment, but it's not going to bring the kind of proceeds that art can. So if a university develops a strong collection, the value of that collection is going to accrue, and it becomes more vulnerable."

This is a point that has not been lost on American universities in, and even before, the economic downturn. Despite a public outcry, in 2008, Randolph College, in Lynchburg, Virginia, sold a painting by the Mexican artist Rufino Tamayo for $7.2 million (?4.3 million), partly to help pay for a new men's sports complex. The school is putting four other works up for auction, including one by the American realist George Bellows, after fending off a lawsuit by alumni that temporarily blocked the sale.

In 2007, Thomas Jefferson University in Philadelphia sold a painting by Thomas Eakins for $68 million to pay for new buildings. The University of Iowa proposed selling a Jackson Pollock mural worth an estimated $140 million to underwrite repairs to its museum, which was damaged in a flood. It backed down only when a report found that such a move might cost the museum its accreditation and the university a substantial amount in future gifts.

A court has cleared the way for Nashville's Fisk University to raise $30 million by selling a half-interest in its collection of art, including works by Georgia O'Keeffe, to a museum founded by the Wal-Mart heiress Alice Walton, after the Georgia O'Keeffe Museum intervened unsuccessfully to stop the move.

This comes at a time when budget cuts, both to museums and their parent universities, have been substantial. This year the University of Wyoming Geological Museum was briefly closed, although it has since reopened part time and without a curator. Other US university museums have suffered deep staff and programming cuts.

At Brandeis, where the Rose Art Museum controversy still simmers, the university was facing a deficit of about $10 million when the board of trustees announced in January that it would close the museum and auction off its more than 7,500 works of art as part of a range of measures that included reducing Brandeis' academic staff by 10 per cent. The university's president, Jehuda Reinharz, called the Rose "a hidden jewel", attracting a relatively meagre 14,000 visitors a year, while its art collection was valued at $350 million - many times the sum required to meet the deficit.

Protests were so great at the proposed move, however, that the university engaged a public relations firm to argue its position. More than 50 members of the family that endowed the museum protested, and three members of its board of overseers filed a lawsuit.

Reinharz announced that he was quitting, although he denied that his unexpected retirement was connected to the Rose fiasco. And although it failed to renew the contract of the museum's director, Brandeis told a judge it would keep the Rose open, at least until the litigation was resolved. It appointed a committee to study its fate and, to assuage the relentless public criticism, put the permanent collection on view.

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The acclaimed exhibition that resulted is testimony to the importance of such art to the academic mission of a university, says Nancy Scott, associate professor of fine arts at Brandeis and a member of the Rose committee. Warhol's images of race riots in the 1960s, which are part of the collection, "have just as much relevance for a student of American history as for a student of art history", she says.

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Scientists, Scott argues, "always get the fancy new laboratories. But a university art museum is comparable to a laboratory. It may have collections of palaeontological remains, human tissue samples or rare books. Those materials have been accumulated by scholars or given by people who wanted to make a donation to the public trust for the education of students."

But lawyers representing Randolph College argued successfully that, unless a gift of art has been restricted in writing by its donor, it is no more or less a part of a university's educational purpose than a hall of residence. University trustees are not only responsible for the financial health of their institutions, they said, they're as free as anyone else to sell off unrestricted assets. If works of art could be considered to be in the public trust, the lawyers argued, so could everything else a university owns, preventing it selling anything.

Furthermore, university museums have not been conscientious about integrating their collections with the academic missions of their institutions. "They did, I think, lose sight of that," Scott says.

"These circumstances over the past few months have driven us to make the case for university museums in a way we haven't done before," concedes Robertson.

University art museums were typically founded by art departments, observes Kimerly Rorschach, director of the Nasher Museum of Art at Duke University, in Durham, North Carolina. "So at the beginning, there was no question about integration. But as these museums got larger and became more professionalised and acquired professional staff, they began to run like professional stand-alone art museums."

Rorschach, who attended Brandeis at the same time as Adam Weinberg, now director of the Whitney Museum of American Art in New York, and Gary Tinterow, now senior curator of European paintings at the Metropolitan Museum of Art, said the debate "has been a learning experience for all of us. Are we closely enough linked to the rest of our universities? Do we have all the right political connections?"

Concerns about museums' integration with their parent institutions predate the most recent controversies. In the 1990s, the Andrew W. Mellon Foundation made grants to 18 US university art museums to help them reconnect with students and faculty. Now the museums are trying to make connections with a vengeance. "The situations that we saw at Brandeis and at Randolph College have really galvanised the field as a whole," Robertson says. "There are many university museum directors who are on notice that their collections may be at risk," Scott confirms. "So they're extremely nervous, and refocused on the theme of interdisciplinarity."

Leading arts organisations including the American Association of Museums, the Association of Art Museum Directors and the Association of Art Museum Curators have also joined forces, recently issuing a statement of solidarity that, among other things, calls on universities to consider their museums "essential to the academic experience and to the entire educational enterprise" and setting up a task force to suggest ways of doing so. The 3,000 signatories to date include some university presidents.

This, combined with the problems at Brandeis, Randolph, Fisk and other universities, may cause higher education institutions to think twice before selling off their art, advocates say. "There has been a very strong public reaction. It doesn't look good in the court of public opinion," says Ford Bell, president of the American Association of Museums.

"The Brandeis president and trustees didn't realise what the cost of this move would be," says Rorschach, who advised the Rose committee but refused to sign its final report because it didn't insist on a guarantee that the museum stay open. "There is a cost, and it turns out to be a grave cost."

Donors, she says, are watching with particular interest - something that tends to get university administrators' attention. After all, says Rorschach, "donors are giving a work of art. It's to help the university's art department, not to be cashed in to build a new basketball stadium."

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