The Department of Education declared yesterday that Alabama, Delaware, South Carolina and West Virginia maintain "vestiges of unconstitutional segregation" in their higher education systems, and gave them 60 days to draw up plans to end it.

The department's findings were based on a two-year investigation of publicly supported colleges and universities in the four states. Assistant Secretary for Civil Rights Cynthia Brown said the department is not alleging the states maintain discriminatory admission policies today, but rather that they failed to integrate separate black and white public college systems that grew up when segregation was legal.

Yesterday's action, expected to be augmented in the next few days by similar findings about Texas, Kentucky and Missouri, tosses a political hot potato into the lap of the incoming Reagan administration. It will now have to decide how to proceed in these cases or whether to back off.

According to one report, the Reagan transition team expressed concern in meetings with department officials that issuance of the finding by the Carter administration just before going out of office foreclosed President-elect Ronald Reagan's options. Brown, however, denied that Reagan aides asked her to delay issuing the findings.

Brown, at a press conference, said the department had no choice but to release the findings now, because federal Judge John Pratt last month ordered the department to make findings one way or the other on these four states, plus Kentucky, Texas and Missouri, by Jan. 15.

The department made these determinations on the four states:

West Virginia has made good progress in dismantling its dual public higher education system since 1954, the date the Supreme Court, outlawed segregation, and has successfully integrated two formerly all-black colleges. But West Virginia University had only 1.1 percent black students and 1.3 percent black faculty in 1978.

In Delaware, Delaware State, the formerly all-black institution, is still three-quarters black, while the University of Delaware is 94 percent white.

In South Carolina, S.C. State, the formerly all-black college, is still almost 99 percent black, while 11 formerly all-white colleges are still 91 percent White.

In Alabama, the two traditionally black colleges are still 88 percent black, and the state's traditionally white public colleges remain 88 percent white.