Under a brilliant full moon just before a bitterly cold West German dawn, the 52 freed hostages stepped back into American life and the warm embrace of a joyful heroes' welcome here today after their 12-hour flight to freedom.

The blinding glare of floodlights and the unrestrained emotion of about 10,000 American diplomats, dignitaries, servicemen and their families and reporters her told them how much they were missed during their 444 days of captivity in Iran.

"Welcome back to freedom," said many of the homemade banners and placards held up for the returning Americans to see. "You're 1/2 Way Home, Baby," another said. "God bless you all," said still another, held up by people in the crowd, many of whom had brought babies and young children with them.

Former secretary of state Cyrus Vance had arrived just hours earlier to greet the freed hostages here. The Carter administration's deputy secretary, Warren Christopher, who headed the U.S. team that negotiated their freedom and greeted them earlier in Algiers, was expected to fly in shortly after them.

The crowd began shouting, applauding, and waving hands and small American flags as soon as they saw the lights of the first C9 Nightingale hospital plane approaching the runway of this air base opposite Frankfurt's busy commercial airport. The freed hostages abroad the planes that brought them on the last hop of their long journey from Tehran, accompanied by Air Force doctors, could see the tumultuous welcome bathed in the bright television floodlights. As the gleaming gray and white C9s taxied toward the crowd, many of the returning Americans began waving to the crowd through the plane windows.

Led by Charge d'Affaires Bruce Lainge, the ranking diplomat among the freed hostages, and Elizabeth Ann Swift, second ranking and one of two women among the 52, they walked easily down the ramps from the planes bundled in gray, fleece-lined Air Force parkas that covered the colorful mix of warm weather clothes seen when they changed planes in Algiers. Although some of them looked quite weary and a bit dazed, they all seemed fit.

Most waved vigorously to the cheering crowd. Some flashed "V" for victory signs or raised their fists triumphantly.

As they were led to waiting blue Air Force buses for the short journey on high-speed autobahns to the hospital in Wiesbaden, some of the former hostages, led by Laingen, veered toward the several thousand service personnel and their families as they cheered before officials ushered them over to the buses.

They were greeted coming off the planes by officials and diplomats headed by Vance and his wife. Each of the freed hostages shook hands with them and some exchanged hugs and kisses.

It took only about 15 minutes for all of them to file into the buses, which then drove off the icy tarmac into the still dark morning as the servicemen and their families sang "God Bless America." West German police brought rush-hour traffic to a halt on the network of autobahns radiating from the Frankfurt airport while the escorted buses made their way to Wiesbaden, an old Rhine River mineral spring resort dotted with U.S. military installations.

The blue military buses pulled up to the Wiesbaden hospital just as dawn was breaking. Many of hospital staff of 800 and their families had crowded out onto the balconies to greet the former hostages. Several patients -- one in a wheelchair and another in a hospital bed -- also were rolled out onto the hospital balconies.

"Welcome to the Freedom Hotel," read a large banner hanging on the front of the three-story building. Yellow ribbons were everywhere -- tied around bushes, trees and railings.

The hospital, part of a huge American military compound in the Frankfurt-Wiesbaden area, represents a bit of America away from home, and the hostages' stay here is intended to help gradually reorient them to American food, American news and other aspects of American life before they return to the United States.

The Air Force hospital, located in a residential neighborhood near the center of the city, was built by Germany at the beginning of World War II and later captured by the Americans near its end.

Deputy State Department spokesman Jack Cannon, who arrived with Vance, reflected the American officials' delight over the release of the 52 Americans, noting that they were no longer hostage and could be called instead "returnees."

"Thankfully, we no longer have to call them hostages," he said. "They are returned colleagues, dear colleagues, from the American Embassy in Tehran. Thank God we don't have to call them hostages any more."

On arrival in West Germany, the freed U.S. hostages received a bubbly, American-style welcome intended to show that many beyond just family and friends cared about what happened to them.

The throngs of reporters and television technicians gathered at the Frankfurt airport where the planes touched down, and more crowded on the sidewalks around the Wiesbaden hospital where they will being to recuperate, alone were a signal to the former captives of the immense amount of popular U.S. and world concern for their fate.

The message of widespread popular interest was underlined by the broad banners and the high-level officials that greeted them at the airport and by the touching drawings done by the children of U.S. military personnel here that cover the walls of the hospital in which they will stay.

After months of isolation, the heroes' welcome for the former hostages were a sign that America did not forget them.

Explaining the U.S. government's interest in keeping the initial welcome low key -- and keeping the hostages out of close news media range -- Cannon said last night, "The American hostages have endured 14 1/2 months of extremely rigorous and terrible time and it is our feeling and that of the medical officers that they need rest and relaxation away from ceremony or press at this time."

At the same time, another government spokesman told reporters that there was no intention to make the former hostages captives again in the hospital here while they undergo a battery of physical and psychological tests. The spokesman said the former hostages would be free to roam around the hospital to stroll outside the 16-acre hospital grounds where reporters and photographers are camped.

A brief tour of the third-floor wing in which the hostages are expected to stay for several days provided a glimpse yesterday of some of the personal touches that have been added to otherwise cold and steely medical rooms to give an especially warm welcome.

Pictures of American flags and houses scrawled in crayon by schoolchildren line the walls. "We missed you," they say, and, "We love you."

One asks: "Were they mean to you? Did you eat O.k.?" Another states: "Welcome back. We really missed you. Free at last."