The Supreme Court, after years of trying to decide when busing should begin, yesterday took up the question of when and how it can be stopped.

The court heard oral argument yesterday on two of its most controversial cases of the year, one from Los Angeles and one from the state of Washington, stemming from the revolt against busing to achieve racial balance in the schools.

At issue in the Los Angeles case is a state constitutional amendment, approved by California voters as Proposition 1, prohibiting state courts from ordering busing except to remedy intentional school segregation. The Washington controversy involves a statewide initiative approved by voters in 1978 prohibiting school boards from requiring busing without court orders.

Both were designed to end ongoing busing plans.

The antibusing measures represent attempts to undo actions that went further than the federal courts require. In Seattle, the school board imposed a busing plan without a court order at all. In Los Angeles, the state courts had been willing to require busing to correct even "de facto" or unintended school segregation, something the federal courts may not do.

Critics of the antibusing measures yesterday attacked them as unconstitutionally racist because they specifically obstruct avenues, federally required or not, used by minorities to combat school segregation.

"Race is written all over the face" of Washington's Initiative 350, said Michael W. Hoge, lawyer for the Seattle school board, which challenged the antibusing referendum there. It is obviously racial, he said, because it allows the use of school buses for transporting handicapped children and reducing school overcrowding and all the conventional purposes except one: to achieve racial balance.

It created "an undisputed racial classification that disadvantages" minority groups and only minority groups, he said.

There was a strong indication during the arguments yesterday that the court might send the Washington case back to a lower court, which struck down the initiative, to consider whether the measure was "intentionally" discriminatory.

Laurence H. Tribe, Harvard constitutional scholar representing the American Civil Liberties Union, led the attack on the Los Angeles proposition with the same argument: it creates a "special obstacle" to minorities obtaining their full rights in the courts of California, he told the justices.

"Just as the Jim Crow laws of the Old South relegated blacks to the back of the bus, this law relegates minorities to the back of the courthouse," Tribe declared. It creates a "two-track" system of justice, one for minorities and one for all others, he said.

Because the measures create "explicit racial classifications," both lawyers said they are unconstitutional under a 1969 Supreme Court decision striking down a law that limited legislative power to enact open housing laws.

If the justices accept this argument, it will have a major impact on school desegregation cases and civil rights policy generally. It could mean that any effort to undo antidiscrimination measures is itself discriminatory because it burdens minority groups.

Lawyers on the other side argued that such referenda do not apply only to minorities but ban busing for many reasons not related to race and apply to all racial groups equally. Arguing in the California case, both the lawyer for the Los Angeles School Board and U.S. Solicitor General Rex E. Lee said Proposition 1 could also apply, for example, to busing of the handicapped.

"But isn't it true that the only real life" application is busing for racial balance, asked Justice John Paul Stevens.

Neither voter initiative restricts the power of the federal courts to impose busing or the power of any court to require busing to remedy intentional school segregation, as would many court-stripping bills now before Congress.

"We have said there is no constitutional requirement to achieve any particular racial balance," Chief Justice Warren E. Burger commented to Kenneth O. Eikenberry, Washington state attorney general.

"That's the state of the law," said Eikenberry.

"But there isn't any law that says they can't" achieve a certain racial balance if they want to, said Justice Thurgood Marshall.

"The Seattle School Board is a creature of the state," said Eikenberry. "The electorate is a super-school board."

Federal courts struck down the Washington initiative as discriminatory. A state appeals court in California upheld Proposition 1 and ended a massive busing plan in Los Angeles in 1980.

"If California loses this case," Solicitor General Lee told the court, "the real losers will be the effort of the states and cities to achieve racial integration" by experimenting with techniques not required by the federal courts. If, having determined that the experiments are unwanted, they cannot then undo them, Lee said they will no longer experiment.