Elated to be back home and proud of a special presidential welcome, more than 6,000 sea-weary Navy men bounded off their ships here this afternoon to savor jubilant reunions with their families.

THE CREWMEN OF THE AIRCRAFT CARRIER U.S.S. Nimitz and the cruisers U.S.S. Texas and U.S.S. California -- fresh from nine long months of sea duty that included participation in the aborted mission to rescue American hostages from Iran -- kissed and bear-hugged parents, wives and other loved ones amid a 20,000-plus throng of family, military and government admirers.

The dockside greeting, which drew more than 3,000 relatives, capped an afternoon of official welcoming ceremonies that the Navy called the largest gathering here since World War II.

Even Navy veterans said they found the Norfolk reception "overwhelming."

David Perry, a yeoman first class on the U.S.S. California, wrapped his arm over his wife Judy's shoulder and pronounced the welcome from Carter "very nice."

Wheeling his 2-year-old daughter, Stephanie, away from the dock, Perry, 26, said today's ceremony was the biggest welcome home in his nine years of Navy Service.

"I came back in '73 after the Vietnam war ended, and it was nothing like this," he said.

Though honored just two hours earlier by a personal visit from President Carter, it was obvious that the sight of their relatives on shore mattered most to the disembarking crew members. Sailors from the U.S.S. Texas, the first of the three ships to dock, lined the cruiser and doffed their hats as the crowd roared.

"It seems more like nine years instead of nine months," cried Phyllis Whaley of Hagansville, Ga., as she cllutched her three children and waited to greet her husband Roy.

For some 200 of the Navy men, today's homecoming was a chance to see new sons or daugthers born while the crews were at sea. For families, sporting buttons proclaiming the men were "worth waiting for," it was a chance to be reassured at least that every one aboard was really okay.

It was from the Nimitz in late April that helicopters bound for the Tehran rescue mission were launched. And the memory of the ill-fated rescue attempt and the continued hostage crisis hung over the crowd but did not mar the welcoming celebration.

"I think we're all supportive of Carter and the country," said Rosemarie Smith, who welcomed her husband, David, home with a special sign to commemorate their eighth wedding anniversary today. "We're proud of our men and we sure all want our hostages back."

The Navy brass and the city of Norfolk made a special effort to welcome the ships. Norfolk's Chamber of Commerce which normally pays scant attention to the Navy base, joined in organizing the dockside greeting by distributing free balloons. T-shirts, buttons and refreshments to relatives of the crewmen.

But there was little of the flag-waving usually associated with a fleet's return. A carnival-like atmosphere prevailed as Navy wives and other loved ones excitedly embraced crew members who had been away from home for the longest sea duty in their careers.

For nine months -- three months longer than planned -- the ships had been away, and much of the time was spent patrolling the Indian Ocean following the seizure of 53 American hostages in Tehran last November.

When the last ship, the 5,000-man Nimitz, docked shortly after 6:30 p.m., friends and relatives squealed gleefully and pumped their welcome signs up and down after catching sight of familiar faces.

And, after a day of balloons, cotton candy, clowns and other pier diversions, children clung only to their daddies when they marched briskly off the ship.

Seaman Alvin Booker, 20, a cook aboard the carrier, held his two-year-old son Johrick's hand and praised Carter for visiting the ship.

"It really lifted morale," said Booker. But he declined to talk about the Nimitz's Iranian operations except to say "we did what was expected, and I wish we could try again."

Relatives of the Navy crewmen began arriving at the Pier 12 docking areas hours before the ships were due in. They lugged blankets, chairs and coolers to vantage points along the waterfront, stretching out in the sun as though they were spending the day at the beach.

Many of the dockside greeters said they decided to join the homecoming celebration after hearing that President Carter would also be on hand. Some families, having driven through the night, had front row seats for the president's address but weren't sure how they were going to spot their husbands, sons or brothers in the crush of sailors and relatives.

"He has no idea we'll be here," said Carol McCurry, who had come up from Greenwood, S.C., with her husband and son to welcome home her brother, Larry Martin, a 21-year-old airman mechanic on the Nimitz.

But Dorothy and Robert Levasseur of Lewiston, Me., the parents of two sons also serving on the nimitz, said they weren't taking any chances. They showed up at the pier with a huge yellow "Levasseur here" sign sure to attract the attention of Danny, 20, and Roland, 19.

A Navy wife, Virginia Garrett, carried a heart-shaped sign with her husband Talmadge's nickname on the front. After 19 1/2 years of such shore rendezvous, she was confident her chief warrant officer husband would locate her and their two children.