When Patricia Roberts Harris became Health, Education and Welfare secretary four months ago, it was said that one of her greatest problems would be the desegregation of state college systems in the South.

Not true.

The problem is heating up pretty much as expected, but Harris is about to hand it off neatly to incoming Education Secretary Shirley M. Hufstedler.

Civil rights officials in Harris' HEW Department are reviewing higher education systems in eight southern and border states. Federal investigators have concluded that at least three of the states -- Texas, Alabama and Delaware -- do not meet federal desegregation requirements, HEW sources said.

Two of the states, Texas and Alabama, could receive notices of noncompliance as early as next month while Harris still has jurisdiction over their cases, sources said.

But the burden will be left to Hufstedler when she takes over fully in the late spring. She must negotiate the politically touchy desegregation issue with unsympathetic governors during a presidential election year.

"We are talking about Jimmy Carter's South here," said one HEW official, who asked not to be named. "Harris may write the letters, but Hufstedler will have to wrestle with the problem."

The problem is that each of the states still has what federal officials regard as identifiably "black" and "white" colleges and universities. Federal law requires action to eliminate such racial identities. That in turn often requires extensive restructuring of some schools, and college desegregation orders have been powerfully resisted in the past.

The penalty for non-compliance can be loss of federal funds, though no such fund cutoff has ever occurred in higher education.

In addition to Texas and Alabama, HEW civil rights officials are currently working on similar noncompliance recommendations for Delaware, South Carolina, Kentucky, Ohio, West Virginia and Missouri. Most of the reviews are still incomplete, sources said.

The cases are undeniably sensitive. Many believe that former HEW secretary Joseph A. Califano lost his job in part because of his insistence that North Carolina conform to strict interpretations of university desegregation guidelines.

The North Carolina case is now before an HEW administrative law judge.

A spokesman for Hufstedler said yesterday that while the education secretary is aware of the civil rights cases, she has not yet assigned anyone to handle them.

Civil rights activists also have been closely watching two other higher education desegregation cases in which Harris is involved. They concern lawsuits against Maryland and Pennsylvania. According to sources, HEW experts have recommended that both states be required to come up with new desegregation plans more stringent than the ones currently in place. The sources said the recommendations were made by the HEW Office for Civil Rights several months ago.

A spokesman for Harris said yesterday that the Pennsylvania and Maryland cases are under review by the HEW general counsel's office and will be passed on to Harris for action soon.

"The secretary is under a court order to proceed and as long as she has jurisdiction she intends to do that," the spokesman said.

However, in interviews this week, officials close to the civil rights cases and others outside HEW expressed concern that Harris may end up shifting the Maryland and Pennsylvania decision to Hufstedler and that any action might then be put off until after next year's presidential election.

Joseph L. Rauh, attorney for the original group of black plaintiffs who raised the issue of higher education segregation in the South, said that if it appears HEW is stalling, he would seek a court order to force speedy action. HEW already has exceeded the time limits set by U.S. District Court Judge John Pratt for completing its review of desegregation plans in several southern states.

The case that is likely to go first to Harris for action is Texas. HEW's regional office in Texas already has recommended that higher education officials there be told to come up with a desegregation plan. Sources said the recommendation could make its way to Harris' desk within the next few days.

HEW officials have been particularly critical of two Texas schools, Prairie View A&M and Texas Southern, which they said were originally established as separate higher education facilities for blacks and which have remained nearly all-black. In the meantime, officials said, Texas A&M, the state's largest land grant school, has almost no blacks.