The Roman Catholic Church has halted the massive losses of its parochial schools that characterized the late 1960s and early '70s and developed an educational system that is drawing increasing numbers of Hispanics, blacks and non-Catholics.

In the last five years, the total number of school-age children has declined 8.2 percent nationwide and public school closings have mushroomed. In that period, the percentage of the nation's children in Catholic schools has remained essentially the same, hovering at about 6.7 percent.

Catholic schools still lost approximately 308,000 students in that time, but that was in dramatic contrast to 1965-76, when rolls declined by more than 2.1 million.

Those figures represent "quite a remarkable turn-around," said Dennis Doyle, formerly of the Brookings Institution and currently assistant secretary for research and improvement at the U.S. Department of Education. s"Even five years ago, people thought Catholic schools were so badly on the skids that they might become a vanishing species."

He sees dual factors behind their recent success and that of other private schools. First, the "widespread feeling" that inner-city schools are in disarray and that suburban schools "are no longer quite as good as they were." Second, the increasing number of two-income families who have "both the opportunity and motivation" to pay for private education.

The lure of Catholic schools under such circumstances, even with tuitions that can run $1,600 and more, is reflected in these statistics over the last 10 years:

The proportion of non-Catholics in Catholic schools has almost doubled, from 5 to 9 percent. (In the District of Columbia, 38 percent of Catholic school students and non-Catholic; in Montgomery County, the figure is now 9 percent.)

Black enrollment is up 21 percent, with the proportion of blacks in Catholic schools rising from 4.9 percent to 8.1 percent.

The proportion of Hispanics in the Catholic school population has risen from 5 percent to 8.3 percent.

"Religion, discipline and academics -- in that order, those are the reasons parents tell us they send their children to a Catholic school, said Leonard DeFiore, superintendent of schools for the archdiocese of Washington. "You get the same reaction all over the country."

It has not been all that easy, however, for Catholic Schools to build on those three blocks in the last two decades, when whole parishes were moving to the suburbs and the teaching nuns, whose vows of poverty had underwritten the school system, were seeking release from their vows or turning to service far from the classrooms.

Even as the church budgets were faced with the tremendous strains of hiring lay teachers to replace the nuns, changes in the church were making Catholic education an option rather than an obligation. Tuition fees soared.

In meeting those challenges, class sizes were substantially reduced; qualified lay teachers, drawn from the growing pool of surplus teachers, were recruited; the remaining nuns were sent back to school for specialized training; curricula offerings were improved, and the schools tried to hold fast wherever possible in inner cities.

Those preparations have helped the schools share in what Doyle described as "dramatic changes" in private education in just the last two years. He explained that the 1979 projections of the National Center for Educational Statistics "predicted level growth" for all private schools, nearly two-thirds of which are Catholic. "But by 1980, they were predicting growth of about 10 or 11 percent."

He predicted that Catholic schools will continue to hold their ground for the immediate future, particularly if some sort of income tax credit legislation is adopted to ease tuition burdens. "But eventually," he said, "the public schools will be shaken into action," such as the establishment of academic high schools proposed by former D.C. school superintendent Vincent Reed.

As the school-age population has continued to drop in the Washington area, Catholic schools have fared far better than their public counterparts over the last five years.

In suburban Montgomery and Prince George's counties, Catholic schools have lost 10.7 percent of their students while public schools were losing 23.9 percent. In D.C., the Catholic schools lost 3.5 percent while public schools lost 22 percent. And in the combined districts of Arlington, Fairfax, Falls Church, Alexandria and Prince William, Catholic schools increased 28 percent, while public schools were losing 9.2 percent.

Some of the reasons for the Catholic schools's comparative success can be seen in such schools as Nativity parish school in Northwest Washington.There was a time when classes of 50 to 60 pupils used to be the rule, but the pastor, the Rev. Andre Bouchard, said today's classes "average around 30 -- the parent's don't like it if you get more than that." The archdiocese's DeFiore points out that the average pupil-teacher ratio for the entire system is currently 23 to 1, roughly equivalent to the public schools.

Most students at Nativity scored "between the 50th and 70th percentile" in last year's standardized testing of elementary school students, according to principal Mayola Lavergne, who added she has also initiated voluntary tutoring classes on Saturdays for seventh and eighth graders in an effort to improve the showing next year.

DeFiore said, "On the average test, the average student [in Washington archdiocesan schools] would be in the 60th percentile" -- 10 points above the national average. "But what's really encouraging is that the longer they stay in the [Catholic school] system, the better their scores tend to be."

Achieving those results can be expensive for parents and school system alike.

Elementary school tuition for local Catholic schools ranges from $300 to $800, said DiFiore; for non-Catholics "it could be as much as double that." Since all schools are subsidized to some extent by the parish that operates them and since persons not members of that parish put no dollars into the offering basket, they are charged a tuition rate closer to the actual cost of educating the child.

Bouchard at Nativity is working on a school budget of $283,999 and expects to keep the tuition for the next year at $800. "This is the time of the year we all [priests responsible for parish schools] start calling each other about the tuition rate so we don't get too far out of line."

Families with more than one child in the school will pay less for the second or third child, the step-back coming in multiples of $200. "After the fourth one, it's free," he said.

Nativity, like a handful of other city parishes here, also counts on the archdiocesan education office for a $10,000 subsidy, which comes out of the archdiocese's $250,000 education budget for schools in Montgomery, Prince George's, Calvert, St. Mary's and Charles counties as well as the District of Columbia.

Gwen Brown, an Episcopalian who has worked hard to put all three of her youngsters through Catholic schools in the District, can attest to their drawing power. "I put up with public schools as long as I could," she said. "I was active in the PTA. But I felt that after working all day, I didn't want to have to come home every night and teach them what they should have learned in school."

Catholic schools, she added, "care about them. If they're absent from school they call you to find out where they are and they have to have a written excuse to get back." She believes Catholic schools "make the students think better of themselves. You see them in the hallways at Mackin [High School where her youngest son is a junior]: they're standing tall; they're not slumped over like they are in public schools."

Their educations have not come without sacrifice. Brown, a computer specialist who is paying Mackin's higher tuition rate of $1,500 for non-Catholics, said, "I've had to do without a lot of things. I've told my children that I'm not going to leave them a house or a lot of money, but I'll give them a good education and a good sense of values."

She thinks the religion courses her children have been required to take in the Catholic schools have been good for them -- "Catholicism is close enough to the Episcopal Church" -- but at the same time, she said, "I make sure they go to the Episcopal Church every Sunday."

Daniel F. Curtin, the principal of Mackin whose student body of about 300 is approximately 35 percent non-Catholic, said the reason parents give most often for sending their sons is "the religious values . . . the value system that's being taught."

I really think that parents see the need for a little better foundation in life than just the academic subject matter," he said, although he agreed with DeFiore that the school's good academic record and the "reputation for self-discipline" also are important to parents.

Religion courses at Mackin, Curtin said, concentrate on Catholic doctrine the first two years and on applied Christian ethics the last two. As in other Catholic schools, all students are required to take the courses, but non-Catholics may be excused from attending mass or taking courses in elementary schools that lead toward confirmation. Curtin and DeFiore said Catholic schools do not pressure non-Catholics to convert.

"In all the years I've been here I've never had a complaint about religion," said DeFiore. "We've had complaints, but not about religion."