A story in yesterday's Business and Finance section incorrectly stated that the Supreme Court had agreed to hear both a California tax case involving the Container Corporation of America and an Illinois tax case. The court agreed to hear the Illinois case.

The Supreme Court agreed yesterday to hear a complex case challenging the authority of states to tax the income of multinational corporations.

The cases challenge the constitutionality of California and Illinois laws that tax part of the combined worldwide income of some multinational firms that operate in those states. They will be heard with disputes the court earlier agreed to hear on similar laws in New Mexico and Idaho. These disputes could have an impact on the taxation of multistate and multinational firms operating around the country.

The California and Illinois cases question whether the imposition of state income tax on the apportioned combined worldwide business income of a group of related companies--including those located overseas--violate the Commerce Clause of the Constitution by creating "a substantial risk of international multiple taxation" and violate the Fourteenth Amendment requirements of due process.

The cases were brought by Container Corp. of America in California and Chicago Bridge and Iron Co. in Illinois on appeal from lower courts that held the worldwide combined reporting method violates neither the Commerce Clause nor the Fourteenth Amendment.

The four cases are seeking to clarify previous rulings on how far states can tax income of foreign divisions of multinational corporations when the parents or other departments may operate in that state while the foreign divisions do not.

For example, in a case involving Mobil Oil Corp., the justices said that, for Mobil to exclude its dividend income from state taxes, it had to prove the income was earned in activities unrelated to Mobil's petroleum products business or whatever business it conducted in that state. Income from out-of-state subsidiaries can be taxed by a state if it reflects profits from a functionally integrated enterprise, the court said. The companies contend in the new cases that their subsidiaries are functionally independent from the business they conducted in the taxing states.

In another case, the justices let stand a lower court's decision preventing the nation's railroads from requiring expensive, special train service when transporting radioactive material from reactors to reprocessing plants, commercial burial sites or waste storage facilities. The justices declined to review an appeals court's ruling that mandatory special train service provided by Conrail and 17 other railroads constitutes wasteful transportation and an unreasonable practice.

Until 1975 all railroads except Conrail handled radioactive materials in regular train service. Some southern and western railroads began handling the wastes in special cars, but the Interstate Commerce Commission later said the expensive service violated the Interstate Commerce Act. Those railroads then complied with the ICC ruling.

However, Conrail then began requiring the wastes to be carried in special trains at higher rates.

The ICC contended that the Nuclear Regulatory Commission and the Department of Transportation, through their numerous safety rulings governing the transportation of radioactive materials, did not require special trains but heavily shielded containers for the materials. An ICC investigation also concluded that no special trains were necessary, and the agency ordered the railroads to provide "a reasonable level of rates."

An appeals court agreed with the ICC, saying ample evidence existed that special train service was wasteful and the rates being charged were unreasonable.