The flagship of the Navy-Marine task force hanging off Cuba's Guantanamo Bay this morning had an unwelcome visitor peering at it through the mist and rain.

An eavesdropping ship, presumably Cuban but flying no flag and designated only by a hull number, steamed toward the stern of the Nassau shortly before 7 a.m., Guantanamo time, to take a close look at the amphibious exercise President Carter had ordered.

Looking through the Big Eye binoculars on the signal bridge atop the Nassau, one could see crewmen standing in clusters on the unidentified ship as the first helicopters roared off the American assault vessel's carrier-like deck.

This was Carter's answer to the Soviet brigade stationed in western Cuba:

Needle-nose Corbra gunships and bulky CH46 troop helicopters thudded their way through the mist and rain squalls that evoked combat scenes from Vietnam.

The Cobras were to provide mock coverage of the landing zones on Guantanamo proper, a Navy base in the heart of Presient Fidel Castro's Cuba, while troopships landed Marines east and west of the center of the base.

The exercise, said briefing officers on this flagship and ashore on Guantanamo, was taged to demonstrate Carter's "resolve" to reinforce the American presence in the Caribbean. The operation cost $500,000. No shots were fired.

Although the Pentagon was eager to do the president's bidding, senior task force officers could have done without a foreign reconnaissance ship taking a front-row seat astern of the Nassau.

Shortly after 7 a.m., the U.S. Navy frigate Hart steamed directly toward the reconnaissance ship bearing the number H-102. As the frigate steamed from Guantanamo toward the eavesdropper, the ship at first held its station about 2,000 yards off the port quarter of the Nassau. Suddenly, however, it swung 130 degrees and faded into the mist well behind the flagship.

Meanwhile, helicopters flew ashore unimpeded by anything but the weather, and amphibious tracked vehicles bearing Marines armed with unloaded M16 rifles ground ashore at Windward Beach without incident.

This same sence of calm pervaded the Marines themselves as they waited for the "invasion" to begin.

"Who's winning the World Series? How did Michigan do on Saturday? Can you gus tell us what this operation is all about?" Those were the typical questions put to two reporters as they made their way through the berthing quarters on the Massau. Country music and rock 'n' roll reverberated throught the quarters.

Not one of more than a socre of Marines interviewed asked a single question about the Soviet comabt brigade, Carter's television speech on in or any other weighty Washington topic.

"About routine," said Marine gunnery sergeant Richard Augherton, 30, of Bristol, Conn., when asked about the exercise today. He was checking out the helicopters to make sure they were fit to make the flight from the Nassau to the landing zones two miles away on Guantanamo's hilly terrain.

Presumably because of the interest Washington policymakers have taken in the mock assault. Marine brass had ordered enlisted men not to talk to reporters unless an officer was present.

Lt. Col. Edward V. Badalato, commander of the 3rd Battalion, 6th Marines, which mad the landing today, denied there was any intent to muzzle his troops. But he said that such orders may have been passed along by his officers through an excess of caution.

The same desire to avoid rocking the Carter administration's boat appraently influenced the way the skipper of the Nassau treated this morning's confrontation with the eavesdropping ship.

"I don't know anything about it," insisted Capt. William A. Kearns Jr., the skipper. "We were so busy here, I didn't see it."

However. an intelligence officer on the Nassau stood alongside a reporter as the two watched the maneuvering of the two ships. Rear Adm. Thomas H. Replogle, commander of the Caribbean Joint Task Force recently established in Key West, said he too had seen the incident while observing the exercise.

The Carter administration intends to keep showing the flag in the Caribbean in such exercises as the one staged here today.

"This is only the first exercise, and I'm sure we'll have quite a few to follow," said Replogle.

The las such reinforcement exercise at Guantanamo was taged in 1975. Carter, in an apparent effort to improve relations with Castro, suspended both Marine ground exercises on Cuba and spy flights over the island until the recent controversy over the Soviet troop presence.

Col. Mark P. Fennessy, commander of the Guantanamo Marine garrison, said that the only big difference between the current reinforcement exercise and the one in 1975 is that the Marines will stay put for about a month after establishing their beachhead.

Of the 1,850 Marines taking part in today's operation, only about 250 rode ashore on the amphibious vehicles, which "swam" from landing barges onto Windward Beach, a spot on the souther coast of Cuba not far from the guerrilla base in the Sierra Madre Mountains Castro used before seizing power in 1959.

A dilapidated camp bult during the Cuban missil crisis in 1962 will be home for almost all the Marines sent in to supplement the permanent force of 423 Marines protecting Guantanamo and its U.S. dependent and contract employe population of about 3,700. The Marines are expected to remain for about a month, conducting a series of tactical training exercises.

No Marine even got his feet wet in the operation, no helicopters crashed and no landing ship went aground. At the end, Fennessy, who passed on the Pentagon estimate that the operation had cost $500,000 above normal operating expenses, said:

"It went like a ballet."