Some drove hundreds of miles and others came from the nearby suburbs. They cheered and applauded and waved tiny American flags. But mostly what thousands of people attending yesterday's parade and the dedication of the Vietnam Veterans Memorial came to do was offer thanks to the veterans of America's most unpopular war.

"We owe 'em a great deal," Eddie Martinez, a 27-year-old employe of the Agency for International Development, said as he watched the parade. "They had this coming to them for a long time. This is our way of saying thank you."

Thousands of others felt the way Martinez did. They clapped and shouted the names of the states as the contingents of veterans -- the small groups such as those from Montana and Kansas and the large ones from such states as New York and Maryland -- marched down Constitution Avenue.

It mattered not how many of the Vietnam GIs were representing each state. They all were applauded with equal gusto, from Alabama's group in the lead of the parade, accompanied by retired Gen. William C. Westmoreland, commander of U.S. forces in Vietnam, to Wyoming's contingent bringing up the rear 2 1/2 hours later.

The older veterans from other wars gone by, their ribbons covering their American Legion and Veterans of Foreign Wars caps, saluted again and again and gave the Vietnam veterans the thumbs-up sign.

The marchers, several thousand strong, often gave back the applause and shouted their thanks in return. One Pennsylvania veteran clasped his hands above his head and shouted to the crowd, "We're home, right here! We're home!"

It was a high-spirited crowd, perhaps not as exuberant as those who welcomed back the American hostages from Iran in January 1981 but nonetheless imbued with a sense of patriotism and genuine feeling for the Vietnam veterans who served, if not always the same feeling for the war they fought.

"It's an historic event," said Colin Campbell III, 36, who edits publications for the International Association of Fire Chiefs. "It's an overdue welcome home for the Vietnam veterans, 10 or 11 years overdue."

"You'll never see the same thing again," said Herbert Yankellow, a 65-year-old claims examiner for the Social Security Administration in Baltimore and a World War II veteran. "It's time to stand up and be counted."

James Barnes, a Capitol Heights resident and an officer in the uniformed division of the Secret Service, said he brought his children to the parade "to let them see what has transpired. I wanted them to see the conditions the veterans went through. This is the first real parade for the Vietnam veterans."

There were many veterans in the crowd who chose not to march, but the day's ceremonies also attracted people from afar who had no direct involvement in the war.

Robyn Jay, a 24-year-old woman from Bloomsburg, Pa., wore an antiwar peace button like the ones so common at the height of the war. But she was ecstatic about the week-long salute.

"They're finally acknowledging the veterans," she said. "It's about time."

Her husband Bill, a serviceman for a gas utility, added, "They did their job and they did it well. Hopefully, it's the last war we'll ever have."

At the dedication ceremonies, Tom Hughes, 24, a computer operator who lives in Arlington, said he came to pay some respect to his brother, a Vietnam veteran. "It's good they're finally honoring the Vietnam veterans," he said. "They weren't given any respect when they returned."

While many of those watching the parade and dedication were lavish in their praise of the veterans, they often condemned the succession of politicians who ran the war from Washington.

"We goofed . . . by not using everything we had to win," said World War II veteran Yankellow. "You don't go in to lose."

Vietnam veteran Rick Moreland of Annapolis stood to the rear of the memorial and lamented the loss of American lives in Vietnam. "There's 57,000 names on the memorial that shouldn't be there because we didn't want to win," he said. "The politicians didn't want us to win."