For the families of the American hostages yesterday, the hours stretched into the longest and perhaps cruelest day yet in their 14 1/2-month ordeal as the crisis teetered back and forth on a cliff edge of resolution.

Finally, as dawn approached the United States, it brought a final message of jubilation out of the east -- the certain, official word that the 52 hostage Americans were airborne at last and winging toward freedom.

One revolution earlier, the sun's arrival here had delivered almost the same euphoria. But then the mood shifted like the image in a cracked mirror. For many hostages relatives, by sunset, elation had drained gradually away into exhaustion and a search for that old companion, patience.

Still, once uncorked, it was hard to get all that feeling back in the bottle.

Henry Metrinko, father of hostage Micahel Metrinko, after he learned that there seemed to be some kind of hitch in the deal, sank from ebullience to what he described as "just struggling along."

Metrinko, who runs a family tavern in Scranton, Pa., turned 70 yesterday. He said he had been hoping for a birthday call from his son. "i could imagine him calling up and I know just what he'd say. He'd say 'happy birthday, Dad.'"

At the Homer, Ill., home of Phillip and Gloran Lewis, parents of hostages Marine Sgt. Paul E. Lewis, a family spokesman said. "They have been trying desperately not to be delighted for 60 hours . . . but this morning they were delighted. [Now] some of the optimism is left but it has been curbed by what is apparently going to be a long wait. I don't think any of us can appreciate the excruciating pain of hanging on from one disappointment to the next."

In Plano, Tex., David Engelmann, the brother of a hostage, sighed wearily as the day wore on. "I'm running on expectancy now . . . . I don't feel too drawn out. I'm sure when we get the word the hostages are on the plane and out of Iran I'll be able to breathe easier."

Some relatives, like Barbara Timm of Oak Creek, Wis., fell into a fatigued sleep in the afternoon. The mother of hostage Marine Sgt. Kevin J. Hermening, she had told a reporter earlier that she had not slept at all the night before and had slept only four hours each of the previous two nights.

Timm, who made a controversial visit to Iran last year to see her son, said she had been on edge ever since she had a funny dream last week. In it, all the hostages were released and came off an airplane attached together like cutout dolls. All except for her son. In her dream, she called the American embassy in Tehran and her son answered and, she said, "I asked him what was going on and he said, 'I decided to stay awhile because I was finishing a puzzle.'"

Yesterday morning, just after daybreak, Hermening's four younger brothers and sisters had hung a banner outside their modest house that read: "Thank you God for bringing Kevin home."

The San Diego, Dorothea Morefield, wife of hostage Richard Morefield, fell asleep right in the middle of a chat with a CBS television producer. She had been "on alert" for 26 hours, giving interviews, serving champagne. On the floor of her bedroon, her 20-year-old son Bill was stretched out in a sleeping bag. Another son Kenneth will celebrate his 15th birthday tomorrow. s

Later, when she awoke and heard about the delay, she said, "Of course it bothers us. We want them off the ground. We want them out of Iran. But I've already said . . . when have they [the Iranians] ever done anything simply if they could find a way to make it more complicated?"

Some families went about their business -- to work, to social gatherings or the like -- as best they could. Several Washington area families attended a preview of last night's inaugural gala with Frank Sinatra at the Capital Centre. Among them was hostage wife Lisa Moeller. Asked how she felt, she said, "Almost relief. But I don't know. I don't know yet." She had finally told her children this morning that "Daddy is coming home," she said. "They were very excited."

In Miami, Judy Blucker, sister of hostage Robert Blucker, appeared at a late afternoon news conference and said, "I've really been pretty numb today . . . not real happy, nor real sad, just waiting . . . I'm really worried until they get out of there."

Margaret Lauterbach, supervisor in a Dayton, Ohio, drycleaners, mother of hostage Steven Lauterbach, seemed determined to keep a stiff upper lip. "I just don't believe I will worry about [the delays]," she said. "I think it is some minor matter of signing something."

Hostage wife Bonnie Graves, at home in Reston, Va., invented her own unusual way to relax away from the cacophony of phone calls and questions and confusions. After she heard about the delay in the hostages' release, she said, she was far from anxious. She went upstairs to lie down in her bedroom and found herself suddenly making up "sort of a mantra . . . . I just thought of the word 'potato,'" she said. "So I got a potato and began rolling around as I was lying down. I rolled it on the floor and over me."

She was not so relaxed a few weeks ago, she said, and when her blood pressure shot up to 165 over 120 (normal is 120/75), she decided to take things easier. "I began turning the TV off, I just wasn't going to listen to it every minute."

Graves had said earlier that she would not be convinced that the ordeal was over until "I can hug my husband. When I can take him in my arms, then I'll know it's over." In the bedroom closet of her patio house is a brand new oversize Rossignole Touche tennis racket and a can of balls for her husband John. "I also made him a warmup outfit," she said. "It's brown velour. I wanted it to be sexy looking."

The returning hostages also will be greeted by a new granddaughter he may not even know about. Kate, born in October, is among the Graves relatives gathered at the family home.

Danielle Golacinski of Silver Spring, sister of hostage Alan Golacinski, said last night that the ordeal has been made even more draining than it might have been by the constant badgering of the news media. At least 50 reporters from around the world had called and some had shown up at the house uninvited, she said, echoing similar complaints from some other hostage relatives.

"They [the reporters] say we're very rude and we owe something to the world," she said. "That's a little hard to comprehend."

Her family was still optimistic despite the delay, she said. "But there's a little bit inside of you that's a little leery . . . . There's always a small percentage of a chance that something might happen."

In a sidelight yesterday, the Civil Aeronautics Board gave the official seal of approval to U.S. commercial airlines who are clamoring to give free roundtrip travel privileges to hostage family members so they can meet the returning hostages wherever they land in this country. CAPTION: Picture, Dorothea Morefield welcomes the news indicating that her husband may be coming home. But the champagne celebration at her San Diego home later seemed premature. After hearing of the delay, she said, "When having they [the Iraians] ever done anything simply if they could find a way to make it more complicated?"