Despite rising costs, increased tuitions and other adversities, America's private colleges and universities are maintaining their enrollments and educational programs, according to a major survey of private schools.

The survey, which draws much conventional wisdom into question, found that while some schools have individually fallen into financial difficulty the overall picture for private colleges and universities is one of stability - no major setbacks, small achievements, no great advances.

But the report found uncertainty for the future as the nation's collegeage population begins to decline.

This was the third annual survey of the private, secondary education industry for the Association of American Colleges by Howard R. Bowen of the Claremont Graduate School and W. John Minter, an educational consultant.

"The fact that there has been no dramatic change in the health of the private sector of American higher education in the three years since we began this study is, to my mind, the most significant thing we have discovered," Bowen said.

In their report, Bowen and Minter wrote: "Despite its acknowledged achievements, the private sector is widely believed to be in serious jeopardy. There are many reports that it faces increasing competition from hundreds of new public institutions, that it has had to raise tuitions substantially year after year so that the tuition gap between private and public institutions has widened; that its income from gifts and endowments has not kept pace with rising costs, and that the pool of available students is contracting."

But, while acknowledging "wide variations in the fortunes of individual institutions," Bowen and Minter found:

Private schools, through the 1976-77 school year, have maintained enrollments in numbers and academic qualifications.

There was no evidence of retrenchment in academic programs and even a slight decrease in the ratio of students of faculty.

Some relief came from the slowing of inflation, enough to make up for some previous cutbacks.

There were more four-year private schools in 1975-76 than in 1969-70, "the very peak of prosperity in higher education."

The private schools remain competitive with public ones, especially when compared with total costs for attending college and students aid programs.

The reports' conclusions were based on a sample of 100 schools designed to represent 866 school, which enroll 73 per cent of the students in private higher education. The 866 schools are four-year, accredited, private, non-profit universities and liberal arts colleges; excluded are major research universities, two-year colleges and specialized professional schools.

The survey included a study of audited financial data, budgets, course catalogs and statistical reports to the federal government, as well as questionnaires.

The report suggests that one way the colleges managed to offset financial difficulty was by allowing faculty salaries to lag behind inflation. Personnel costs are the biggest expense for colleges and universities.

So, Bowen and Minter wrote, "Perhaps the most important finding of this year's study is that employment - both academic and nonacademic - expanded. This together with salary increases approximately the rate of inflation suggest that the private sector is not being forced to retrench significantly."

Their conclusion on the future are gaurded; inflation rates are unpredictable, the college-age population will decline, and there is a growing emphasis on more technical education. Also, they found, past financial problems were salved by delaying the construction of new or replacement facilities "and a day of reckoning . . . will come some day."

"Every serious observer of private higher education knows that the position of private universities and colleges is precarious," Bowen and Minter wrote. "The institutions report overwhelmingly that their staying power has been due in part to the growing state and federal programs of aid to students and to students and to institutions," careful management, donors and appeals.