IT WAS 11:30 in the morning when Walter Cronkite announced over CBS radio that the hostages were airborne. Hal and Dee Thornton of Burke, Va., and their son Shawn leaned closer to their portable radio set up on the sidewalk across from the Commerce Department building in downtown Washington. They smiled and began applauding. Two police officers bent over to listen better. A ripple of applause rose from the inaugural parade crowd, and then a loud groan. The hostages, said Cronkite, were still on the ground. "They're going to hold them right to the time Reagan's sworn in," Hal Thornton said tightly.

The tense countdown to freedom had a special meaning to the Thornton family yesterday. Hal Thornton is a major in the United States Army. He was a military adviser stationed in Tehran, assigned to teach the Iranians how to use American military equipment. His wife and children were evacuated from Iran in December 1978, when conditions began to deteriorate. Two months later, he and other military personnel were evacuated after the first takeover of the American Embassy by Iranian militants. They, too, had waited hours to leave the airport in Tehran, and they, more than most Americans, had a special sense of what the hostages were going through. Having been so close to a country on the edge of political disintegration, the Thornton family came to Washington yesterday to celebrate the peaceful transition of power that is the American way. "We are," said Hal Thornton, "very fortunate to have this kind of country."

The Thorntons still find it difficult to understand what happened to Iran. "They didn't treat me with hatred when I was there," said Dee Thornton. "I don't want to hate the Iranian people. I don't want to hate anybody. But it's very difficult not to get terribly frustrated and angry."

And as the minutes passed and the delay and uncertainty continued, she looked out at the gathering crowd on Pennsylvania Avenue and echoed the thoughts of many. "It's so nice to be here," she said. "I'm an American and I can stand here. I don't have a gun pointed in my face."

"You can express your disagreements," said Hal Thornton. They are, he said of his family, participators. They would have come for the inauguration even without the developments in the hostage crisis that made yesterday one of the most extraordinary days of modern times. And when Sen. Mark Hatfield asked the crowd to join hands in an affirmation of new hope, the Thornton family members extended their hands to those around them and stood silently as Marine Corps Sgt. Michael Ryan sang "America the Beautiful." Dee Thornton blinked back tears.

"The frustration factor is so high that everybody is looking for something," said Hal Thornton. "This will give them new hope." And when President Reagan told the crowd that its hopes, its dreams and its goals would be the hopes, dreams and aspirations of his administration, Thornton nodded and said quietly, "He's very eloquent."

Reagan spoke to the hearts of people lining the parade route, people who had come to celebrate him, their country, and themselves. And when he spoke of freedom they applauded, and when he spoke of peace without surrender, they applauded, and when he was finished, their thoughts returned to the final moments of the drama being played out so far away and so far beyond their control.

"The people there are very impetuous," said Hal Thornton. "They are people who are quite capable of changing their mind at the last minute." And so the crowd waited, listening to radios, until the word finally came at 12:42 p.m. "Wheels up in Tehran," said the announcer, and the applause and cheering came at last. "All right!" said Hal Thornton, his face breaking into a tremendous grin.

This was not Jimmy Carter's day, but the people in the crowd did not forget him. They were distressed that he could not have freed the hostages while still president; sad that he had been robbed by minutes of a special place in history. Yet they knew he was leaving them with a lesson they would not soon forget, a lesson of what can be accomplished by a peaceful nation that is strong enough to be patient.

"It would have been nice for him to have been able to say they were free," said Jean Kaufman, who came in from Potomac with her three sons. It has been, she said, an exciting time in our history, and now she believes there will be an upswing. "Hope rather than despair."

Hope stayed in the air long after the sun vanished behind clouds in the afternoon, long after the parade should have started. And when the U.S. Army Band finally marched by, playing, "When the Caissons Go Rolling Along," the applause was from the heart for a president who symbolizes the new beginning Americans want.

"I wouldn't have missed this for anything," said Hal Thornton. "He is president of the United States. He is the man who has the responsibility for this country.

"I'm proud of him and of what he represents."