The horses stepped high down Pennsylvania Avenue in perfect cadence with the high school bands. Drill masters shouted, "Step lively!" and the marchers did, their shoulder tassels bouncing to the beat. The crowd -- singing, clapping and waving American flags -- slapped hands on neighbors' shoulders and cheered and cheered and cheered.

Finally, yesterday afternoon, after a week of limousines and private inaugural parties, it was the people's turn to have some fun.

More than 300,000 Americans from the nearest and farthest corners of the nation converged on the avenue for President Ronald Reagan's inaugural parade simply to celebrate, both the parade itself and the hostages' freedom, and they did it with unrestrained jubilance.

"This is it!" This is what the country is all about! shouted Adrian Martin, a textile worker from Scranton, Pa., as he watched Reagan's motorcade glide past him on 14th Street NW and heard the people roar.

"Damn, it's great to be here."

From the people in jeans and earth shoes standing 10 bodies deep at the Capitol to the sable coats and pinstriped suits sitting jampacked on 15th Street bleachers, spontaneous cheers erupted. As temperatures hovered pleasantly in the fifties, portable radios crackled with the news of the hostages' release from Iran, panhandlers worked the crowds like entrepreneurs, and sidewalk vendors hawked everything from "Freedom" T-shirts to Reagan political buttons.

The crowd joked and bantered as the processions passed. "Danny," exclaimed 5-year-old Shannon MacGregor as she sat atop her brother's shoulders, "Did you see what those horses keep doing in the street? Who's going to clean it up?"

With the ironic theme, "America -- A Great New Beginning," Reagan's parade started an hour and a half late and didn't end until shortly before 5 p.m. It include more than 8,000 marchers and musicians, 25 Alaskan sled dogs, 450 equestrian teams, three floats and color guards and guncarrying marching units from each of the military services and their academies.

Reagan, who witnessed the parade from a reviewing stand in front of the White House, desired a "short, snappy parade." An equestrian, he also requested horses, and often during the parade, when a team of them passed by, he smiled, pointed and tapped his wife on the arm.

The parade was pure Americana, with lively, soulful black marching bands, Indians in native dress on horseback, mountain men carrying muskets and wearing coonskin caps, and patriotic songs -- "This Is My Country," "God Bless America," and "Anchors Aweigh."

Reagan reacted most enthusiastically to a band representing Dixon (Illinois) High School, from which he graduated. He stood up from his seat when they passed in their purple and white marching outfits, and waved a cowboy hat he had by his side.

The spirited crowd clapped hands in time with the military marching bands as they stepped up Pennsylvania Avenue playing military theme songs. "We are reacting this way because we've downplayed the strength of this country for so long," said Jackie Wise, a technician for the Bureau of Standards, as the crowd cheered the Marine Corps band playing "The Marines Hymn."

The spirit on Pennsylvania, if not in affection for Reagan, was definitely for parades and music. On the parade route Gwendolyn Washington of Southeast Washington was trying to manage a small parade of neighborhood children herself. "We are here to see the parade, that's it," Washington said firmly. "Just to see the setups."

Her young daughter added sweetly, "We came to see the president, mama."

"No we didn't," her mother shot back coldly. "We can't stand that man."

They came from as far away as Oregon and California to witness what many called a once-in-a-lifetime chance to see an inaugural parade, including one man, Charles Pague from Shippensburg, Pa., who arrived in Washington by Greyhound bus last night and spent predawn hours at the bus station downtown.

"I have my camera. I just want one click of this," said Pague. "I really feel like an American being here."

After a week of anxiety over events in Iran, and after so many fancy, invitation-only inaugural parties and galas, it was truly the people's chance to party.

"My office overlooks Connecticut Avenue and all this week I've heard sirens and limousines," said Jeffery Levine, a 23-year-old Department of Labor worker. "It's neat to be here."

Meanwhile, the parade went on. Crowds lining the sidewalk broke into little jigs as the Marching Jukebox of Southern University tooted "Bourbon Street" and "Way Down Yonder in New Orleans."

In front of the District building, they roared loudest for the hometown's Cardozo High School marching band. They oohed and aahed as the Alaskan husky sled dogs huffed and puffed and pulled a sled of men in coonskin hats.

They laughed and clapped as a red, white and blue float replete with dozens of young girls in tight white outfits passed by and released dozens of hot air balloons attached to an American flag. In the middle of the march, men in Mexican sombreros on horseback waved their wide straw hats at Reagan, prompting more laughter and cheering. And then there was the New York City Mounted Police who galloped up Pennsylvania waving flags festooned with the slogan, "I Love New York."

Although the sun retreated behind darkening clouds yesterday afternoon, the rain that was expected didn't fall. And when it was all over, after the Mormon Tabernacle Choir sang "The Battle Hymn of the Republic" in front of the presidential reviewing stand, the crowd and the participants headed their separate ways, including the parade's American Indians, who boarded a van and held a buffalo barbecue cookout on the Mall.