More than half the black children born in the United States during 1976 were born to unmarried women, according to a new report by the National Center for Health Statistics.

It was the first year, officials said, that black births out of wedlock exceeded 50 percent of all black births, although the number has been rising steadily for more than a decade.Just 13 years ago, 26 percent of all black children were born out of wedlock.

The new statistic is the latest indicator suggesting significant changes in the structure of black families, and researchers in the field are more certain of the importance of the changes than the reasons for them.

"The real changes that are taking place during the 1970s are just enormous," said Kristin Moore, a researcher at the Urban Institute. "The changes are so rapid that they've caught us all out. No one can say definitely why it's happening."

Today, 40 percent of all black children live in families headed by women, compared with about 12 percent of white children. Six years ago, the figure for blacks was 30 percent.

Almost one-third of all black children now receive benefits from Aid to Families with Department Children, the $11 billion-a-year federal welfare program for broken families.

The latest report says that 258,000 children were born to unmarried black women in 1976, about 9,200 more than in 1975, and accounted for 50.3 percent of all black births.

Even though the proportion of out-of-wedlock births edged over 50 percent, the birthrate among unmarried black women actually declined. However, the number of such women continued to expand rapidly, while births to married black women continued to drop.

The same phenomena are occuring among white women, although on a smaller scale.

Out-of-wedlock births have risen, the report said, to 197,000 or 7.7 percent of all white births in 1976. The proportion of white births that were out of wedlock was 4 percent in 1965.

The birthrate for unmarried black women aged 15 to 44 (the years of female fertility, according to health statisticians) dropped by 13 percent between 1970 and 1976. However, the number of unmarried black women in that age group soared by 38 percent as divorces surged, the average age at marriage rose, and the children of the 1950s baby boom reached maturity.

At the same time the number of married black women aged 15 to 44 rose by only 1.7 percent. Their birthrate dropped by almost 30 percent over six years to 91.7 per 1,000 women in 1976.

According the new report, married black women in the United States now have a slightly lower birthrate than married Whites for the first time since such statistics have been compiled. The rate for married whites was 92.0 births per 1,000 women in 1976.

Among unmarried women, however, differences between the races are still wide. In 1976 there were 83.2 births per 1,000 unmarried black women, compared with 12.7 births per 1,000 unmarried whites.

Teen-age mothers accounted for about half of all the out-of-wedlock children born to both black and whites in 1976, and they are the only age group for whom the rate of out-of-wedlock births has increased.

In addition, fewer single teen-agers who become pregnant now are getting married before the child is born, said Arthur A. Campbell, deputy director of the Center for Population Research at the National Institutes of Health. It is still more prevalent for pregnant white teen-agers to marry before the child is born than for blacks.

Although the stigma of out-of-wedlock births has probably declined, John Kantner, chairman of the Department of Population Dynamics at Johns Hopkins University, said suchbirths still carry substantial disadvantages for both the women and children involved.

The Urban Institute's Moore said about 60 percent of all out-of-wedlock children receive public welfare aid at one time or another.

"In that sense out-of-wedlock births really are a public problem," she said. "It really is harder for children to be in families with low incomes. I think it's the income, not the marital statue, that causes problems [for out-of-wedlock children]. But low income is related to the fact that they don't have a father in the family with the type of income that a man has in this country today . . . Female-headed households are ocr new poverty group."

One puzzling aspect about the increase in out-of-wedlock births, Kantner said, is that it has occurred despite the legalization of abortion.

From 1970 to 1972 - the first year when legal abortions were widely available - white out-of-wedlock births did fall by about 9 percent. But they have increased every year since then.

Among blacks out-of-wedlock births have risen every year since 1965.