Congressional hearings are scheduled and a General Accounting Office investigation has begun into the Federal Aviation Administration's multimillion dollar development program of an advanced guidance system that would safely land planes in all kinds of weather.

Rep. John Burton (D-Calif.), chairman of a House Subcommittee on Government Activities and Transportation announced the hearings for Jan. 31 at the same time the GAO confirmed for The Washington Post that it had begun an investigation.

The centerpiece in both discussions is charges by the British that the United States, in effect, film-flammed an international selection committee into favoring a U.S.-developed landing system over a British-developed landing system. A final international decision is scheduled to be taken in April.

Both British and American systems currently are being demonstrated at various airports. The FAA recently mounted a demonstration for the press and officials at John F. Kennedy International Airport in New York. Data from those tests is to be considered before the final decision is made.

The purpose of all this is to develop one international standard for all-weather landing systems so aircraft in international flights will not have to be equipped with a different decoder for each country.

As a result of the most recent American tests, the British have raised new questions about the validity of the U.S. system. A high British defense official, in a letter to his U.S. Air Force counterpart, said that on a flight he took on the U.S. system in tests at Buenos Aires, "there was a pronounced weave and roll . . . and the aircraft ended up each time badly misaligned from the runway . . ."

The British also have charged that the U.S. won the recommendation for its system with equipment that has never been proven. "Only the most complex and costly version" of the N.S. system, the British say in an official paper, "can satisfy the accuracy and coverage requirements" of a new guidance system. The British system they claim, can do the job more cheaply.

Critical to the U.S. system's alleged economic edge is a device known as a COMPACT antenna. J.W. Cochran, the FAA's associate administrator for engineering and development, confirmed yesterday that there is no operational COMPACT antenna. Such a device was part of the equipment package presented by the U.S. when it won a preliminary international recommendation for its system.

The British have been studying thousands of documents from the FAA that they received after congressional pressure was placed on the FAA to make all information available.

All the papers recording test flights on the latest generation U.S. system are stamped with the words "This data does not represent normal equipment operation . . ." due to various reasons. If that is all the data, the British are asking, what is the basis for the claim that the U.S. system works.

Cochran, asked about that, said the British selected what they wanted from the data available. Further, he said, the international recommendation for the U.S. system was based on earlier generation equipment.

British officials have been invited to testify at Burton's hearings, but have not answered the invitation. If they choose to do so, it would be unprecedented.

The GAO is investigating the matter, according to Jerome Stolarow, because "we're primarily interested in why a new system" is needed and whether the expenditure is justified. Cochran puts total U.S. development cost at $110 million.

"It's vital to expore this controversy now," Burton said," . . . because American integrity is at stake."