There are few students these hot summer days at tiny Fisk University, a 117-year-old school built on the site of a slave market. But the campus still flowers with a richness of black history and academic achievement.

Outstanding minds--W.E.B. Du Bois, James Weldon Johnson, Arna Bontemps, Alex Haley--have taught or studied in the shadows of the white clapboard Little Theater, an old Union Army barracks, and Jubilee Hall, a faded brick Victorian named for the Fisk Jubilee Singers who introduced the world to the black spiritual.

The lawns and hedges are well-trimmed, and the administration building's buffed granite floors glow beneath Gothic portals and along corridors adorned with bold African sketches.

But the sense of well-being is deceptive. Fisk is fighting for its life--as are many of the nation's 103 traditionally black colleges and universities. In 1960, they educated two-thirds of all black college students; today, they educate one-sixth.

In the past two decades, cheating death has become an increasingly common problem for historically black colleges and universities, whose obituaries were first written when historically white schools began to integrate.

Corporate donations are harder to come by and endowments are virtually nonexistent for most black institutions. Competition for foundation funds is more intense, and so is the battle to attract top black students and faculty.

In addition, federal cutbacks in financial aid, real and threatened, are cutting the lifeline for many of the institutions' poorer-than-average students.

Last year there was a 12 percent drop in freshman enrollment at the 42 predominantly black private colleges of the United Negro College Fund--three times the national average--and their overall enrollment dropped 4 percent, compared with a national average of less than 1 percent.

Fisk typifies the problem. Enrollment is down from 1,500 in 1971 to 757 last fall. Eroded by years of borrowing to finance operating deficits, its once nearly $15 million endowment now stands at $4.5 million.

Rustic brick walls, majestic stone steps and Gothic towers and even parts of historic Jubilee Hall are crumbling. Memorabilia donated by Haley to his alma mater are collecting dust in the office of university President Walter J. Leonard.

Earlier this year, a frustrated faculty assembly gave Leonard a vote of no confidence after he informed them he no longer could promise to never miss a payroll.

No payrolls were missed, and Fisk hopes to finish the year without a deficit. Moreover, Leonard's six-year recovery plan is showing some success, and a revitalized board of trustees has launched an $18 million fund drive with $100,000 from its own pockets.

Still, there is an eerie sense of the past repeating itself. Leonard said recently that Fisk has been "historically black, proud and poor"--down but not out. This appears to be another of those times.

That view is echoed by Christopher F. Edley, executive director of the United Negro College Fund.

"We're pretty much in the same shape we've been in throughout the '70s--hard pressed for money but surviving," he said. "It doesn't do us any good to have people talking about private black colleges in dire financial straits," Edley said. "We've always been in dire financial straits."

Across the street from Fisk, Meharry Medical College, alma mater of 40 percent of the nation's black doctors and dentists, was rescued last year when the federal govenment forgave a $29 million debt on a federally insured mortgage.

Still, the size of entering medical classes has been trimmed from 110 to 80 and many newer students must take out high-interest loans because the federal scholarship program for medical students who plan to work in underserved communities--as 75 percent of Meharry's graduates do--has been eliminated.

"I believe that all of the historically black colleges in this country are in jeopardy unless they're getting substantial federal funding," said Meharry President David Satcher. "I just don't think that we have the financial base right now to say that we're out of danger financially."

Integration has had its effect, too. Three historically black schools--Bluefield (W. Va.) State College, West Virginia State College in Institute, W.Va., and Lincoln University in Jefferson City, Mo.--have become predominantly white institutions.

Here in Nashville, historically black Tennessee State University has swallowed up the former University of Tennessee-Nashville in the wake of a merger ordered by a federal judge in 1979.

In the process, TSU increased its enrollment by 60 percent, added a new dimension to its course offerings and is now using a $100,000 scholarship fund to recruit minority students--whites--to help integrate its 63 percent-black student body. Before the merger, TSU's student body was 85 percent black.

"With the merger, our mission certainly was broadened," said TSU President Frederick S. Humphries. "We are now a multi-racial institution and our mission became enhanced to include an urban thrust, which we did not have before."

Despite such changes, historically black schools still produce more than 31 percent of the nation's black college graduates, and an estimated 40 percent of the blacks who teach in college are on the faculties of black institutions.

"Blacks have a lot of bad experiences in white institutions," said Kenneth S. Tollet, director of the Institute for the Study of Educational Policy at Howard University in Washington, D.C.

"There's nothing wrong with integration in principle," he said. "It's just in practice."

At Howard, another traditionally black university, the number of students transferring from other schools increased by 26 percent last year and many of the transfers appeared to come from white schools, said William H. Sherrill, Howard's dean of admissions and records.

Last year, Howard enrolled 2,155 new freshmen and 1,076 undergraduate transfers. The year before, there were 2,783 new freshmen and 855 transfers.

In the South, some first-generation black graduates of integrated high schools are setting their sights on black schools at the undergraduate level and beyond.

Biology major James Whittaker, 19, of Columbia, Tenn., attends historically black Lane College in Jackson, Tenn. He has three preferences for medical school, he says: Meharry, Howard or Morehouse in Atlanta--all traditionally black schools.

"I think I can associate with white people. I went to a white school, I was vice president of the senior class. I'm able to communicate with white society and I can deal with whites," Whittaker said. "It's not that I would be going to a 'white' school or a 'black' school. It's just where I would feel more comfortable," he said.

Ann Slaughter, 20 and a senior at Fisk who, like Whittaker, attends a United Negro College Fund-sponsored premedical summer institute at Fisk, is a graduate of a predominantly white Catholic high school in Chattanooga.

"Everywhere you looked, it was white, rich white kids. That's not reality," she said. "I knew I wanted to go to a black campus because I'd never gone to school with black people . . . . I wanted to be with other black people who are going to become the stars, the future Alex Haleys, the future doctors and all that."

Many black college officials feel put upon when asked to defend the legitimacy of schools like theirs.

"People ask you, 'Why do you need Fisk?' Why do they ask that question?" said Meharry President Satcher. "Most of the institutions in this country were founded with a narrow focus and they were expanded over the years."

"I don't think that question should be asked any more than you ask, 'Why do you need Georgetown a Catholic university ? Why do you need Brandeis a Jewish university ?' You only hear those questions about the historically black institutions," Satcher said.

"We'd love to have more white students," Fisk's President Leonard said. Fisk has about two dozen now. "But unfortunately, society has said to a white student, 'Well, that's a black school and you don't really want to go to a black school.' "

Some blame the Reagan administration for the current woes of historically black colleges. Critics contend that while it launched a highly touted initiative in 1981 to preserve black schools, it is hurting them by cutting back on student financial aid.

Last year, for instance, the administration obligated $564.5 million to black colleges in grants and contracts, an increase of $19.6 million or 3.6 percent over the previous year. This was at a time when obligations to all colleges and universities decreased by $176.9 million.

Some of largest amounts went to a handful of colleges, including Howard ($145.2 million, or 26 percent of the total), Meharry ($29 million) and Tuskegee Institute in Tuskegee, Ala. ($9 million).

Despite the increased funding, Mary Carter-Williams, senior research fellow at Howard's educational policy institute, said black colleges still receive a disproportionately small share of grants for scientific research--2.1 percent of the $4.6 billion awarded overall.

But most harmful, she said, have been reductions in student aid, which is more critical to blacks than whites as a source of funds for higher education.

Between 1981 and 1982, appropriations for the federal Pell grant program (the old Basic Educational Opportunity Grants) decreased by 7 percent and funds for campus-based assistance declined by 4 percent. Reagan's 1983 budget threatened to reduce allocations in both areas, but Congress rejected the cuts and the 1983 funding remained the same as for 1982.

All of this has occurred, Carter-Williams said, at a time when the black college-age population is increasing, the white college-age population is in decline and pinched pocketbooks among the middle class have diverted attention from helping the poor.

"In light of the economy changing and Americans being concerned about inflation and the rising cost of living, we've had a shifting down of educational opportunity as a public value," she said.

However, Edward M. Elmendorf, assistant secretary of education for post-secondary education, said that despite any cuts, Pell grant formulas allow students at black colleges who are poorer than white counterparts to get an average of $200 more per grant.

Elmendorf said that as a result of the administration's black college initiative, obligations should surpass $600 million this fiscal year. And although the administration favors streamlining on-campus aid programs, he said, it is not reducing spending.

"I feel it's well on the way to working," he said of the administration program. "We have the dollars to show it."

Some problems of black institutions can be traced to successes of the civil rights movement. At Meharry, for instance, many patients who previously could go nowhere but to a black hospital now go to white facilities--and often are sent by black doctors.

Consequently, Meharry's recently built teaching facility, George Hubbard Hospital, was half empty for some time. That helped create the college's $29 million debt and also threatened the facility's accreditation because there were too few patients for proper student training.

"I think that's good that black physicians have options," Meharry President Satcher said. "I think the unfortunate thing is that integration is uni-directional. We haven't seen white physicians coming to historically black hospitals and admitting white patients in great numbers."

Satcher and Leonard also hold alumni partially responsible for not giving substantially to the schools that educated them.

"The historically black institution does not reflect the economic, social and political performance or achievement of its graduates, unlike the white institutions," Leonard said. "We have several graduates who have a net worth of a million dollars or more who don't give anything."

Leonard said part of Fisk's problems began in the late 1960s and early 1970s, when it expanded its student body and course offerings too quickly, overextended its assets and lowered its academic standards in an ill-fated effort to bolster the university athletic program.

Drastic steps toward recovery were taken in 1974, when about 40 percent of the faculty and half the staff were laid off, he said. Since 1977, when Leonard became president, the university has been struggling to keep above water.

"Financially," Leonard said, "Fisk always has been underfunded, to some extent unwanted, to a great extent feared. There has always been an attempt to make Fisk less than what it can or should be."