Along with the crowded terminals, overflowing parking lots and congested runways at National and Dulles International airports, the federal government also has left the new airport authority with a broken-down system for monitoring aircraft noise, according to a Metropolitan Washington Council of Governments memo released yesterday.

COG's board urged the new Metropolitan Washington Airports Authority to design and install a system to record, measure and analyze aircraft noise, which has been the source of constant complaints from residents near National.

Antinoise activists have expressed hope that the authority, governed by a board of local representatives, will be more responsive than the Federal Aviation Administration, which operated the government-owned airports until Sunday.

The FAA built a noise monitoring system in 1976 that comprised 23 outdoor listening devices to record aircraft sounds, and a computer system to analyze the information. The system is now "nonfunctional and obsolete," according to a memo by Stuart A. Freudberg, COG's director of environmental programs.

Many of the 15 microphones monitoring aircraft noise at National and eight monitoring Dulles are broken. The devices that do work are useless because the computer no longer works, council staff members said.

A new system will cost from $500,000 to $1 million, according to estimates by the authority, which already faces the task of financing $700 million worth of other improvements at National and Dulles.

Now that they are free of federal control, the airports are eligible to apply for federal grants for the noise project, said Sue F. Silverman, the authority's director of community relations.

A. Linwood Holton Jr., chairman of the authority, told COG's National Airport Noise Abatement Committee that "I just want to assure everybody that we understand the concerns of the citizens . . . and we want to hear your suggestions." The board, at its July 1 meeting, plans to discuss a proposal to create a citizens advisory committee to advise the board on a variety of issues, including noise, he said.