Nearly one-third of the American men and women who are living together but not married are raising children, the Census Bureau reports.

Of the 2.33 million unmarried couples across America, some 720,000, or nearly 31 percent, were raising children as of March 1987, the bureau reported Thursday.That's up from 2.22 million unmarried couples, 662,000 with children, reported a year earlier.

In addition, the new report on "Marital Status and Living Arrangements" found some 1.55 million couples of the same sex living together, including 92,000 with children. That is up from 1.47 million same-sex couples a year earlier, also including 92,000 with children.

A same-sex couple could include anything from a parent and an adult child living in the same household, homosexual partners or individuals who happen to share living quarters. The Census Bureau does not ask the sexual preference of individuals.

Arlene F. Saluter, of the Bureau's Population Division, said the data in the new study showed a continuation of the general trends of recent years, with no major corners being turned. For example, the study found:

-Among children under age 18 nearly one in four (23.9 percent) lived with just one parent, up from 23.5 percent in 1985.

-There were 130 divorced Americans for every 1,000 still married and living with their spouses, down from 131 in 1985.

By comparison, figures released last fall showed more than 51.5 million married couple households in the nation in 1987, up from 50.9 million a year earlier. That, too, has been rising as the massive post World War II Baby Boom generation forms families.

While the vast majority of the unmarried couples are younger people, the category also includes others, such as elderly widows who rent rooms to college students, Census officials note. Unmarried couples are simply defined as two unrelated individuals, of the opposite sex, who share a housing unit.

Of the 1987 unmarried couples, 1.41 million listed a man as the householder - formerly known as the head of household. Of those, 395,000 households included children. In addition, 922,000 unmarried couples listed the woman as householder, including 325,000 with children.