The Navy has just given the public a rare glimpse of the frustrations of waging the Cold War by telling Congress that trawlers are ripping up the secret eavesdropping system the United States has laid on the ocean bottom.

Things have gotten so bad out there in the depths, Adm. James L. Holloway told the Senate Armed Services Committee in testimony recently made public, that the Navy needs to build a $191 million ship to keep the underwater listening system in working order.

Although some Navy officers grumble that Soviet trawlers are breaking up the submarine warning network on purpose, this was not the official Navy position when the service was queried by The Washington Post yesterday.

"Fishing trawlers from various nations" have broken the transmission cables that connect underwater microphones to receiving centers on shore, the Navy statement said. "These occurrences are not considered to be deliberate. We cannot confirm that any of these trawlers have been Soviet."

The Navy underwater warning network, once a closely held national secret, is called SOSUS, for sound surveillance system. The underwater microphones pick up the ocean sounds for hundreds of miles around and send them through the cables to low buildings behind chain link fences spaced along the Atlantic Coast.

In a bit of computerized detective work that the Soviets cannot yet duplicate, the United State intelligence apparatus sorts out the sounds SOSUS picks up and identifies the distinctive noise of any passing Soviet submarines.

Thanks to other stealthy eavesdropping under the sea, computers have been fed the noises each of the operational Soviet subs makes as it prowls unseen under the waves. So SOSUS can tell which sub is out there and in what direction it is headed.

In a period of international crisis, knowing the location of Soviet subs within missile range of the United States would enable destroyers and anti-submarine planes to rush to the spots for possible combat.

SOSUS is considered a vital part of the nation's early warning system against Soviet submarines. Holloway, chief of Naval operations, told the Senate Armed Services Committee in his testimony released last week that he considered buying a new ship to keep SOSUS cables repaired as important as buying a new warship.

"The capability of the SOSUS system," said Holloway, "the sound array system that permits us to detect the location and presence of Soviet submarines, is largely dependent upon our ability to use those cable repair ships to repair breaks that are occurring with increasing frequency as the result of trawling operations."

Those undersea warfare specialists who believe Soviet trawlers are deliberately breaking SOSUS cables contend it would not be hard to do. Soviet agents in the United States or Soviet reconnaissance satellites most likely could determine the direction the cables took after leaving the coastal station, these specialists said.

However, other officials theorized that the Soviets are not concerned enough about SOSUS to risk an international incident by sabotaging it.