Down Constitution Avenue they came to claim a place in their parade. Most had never met before, but they marched in perfect step. By their own description, they looked like "ragtags," with makeshift uniforms of crumpled jungle fatigues.

But as they moved toward the Capitol, in the quiet hour before the procession, they were already inviting faint applause from Memorial Day stragglers. "This is the Vietnam vets that survived the Vietnam War," proclaimed one. And defiantly, he refused to explain how this group of hirsute and untidy veterans came to be walking together, in cadence, toward the foot of Capitol Hill. "This is the Vietnam vets that survived the Vietnam War," he yelled again.

Their Memorial Day pilgrimage had been improvised, a fitting testament for a war many of them later felt was chaotic and senseless. Yesterday morning, while visiting the Vietnam Memorial, they talked and found they needed to be part of the cortege that would lay their fellow soldier to rest.

"I've never seen anything like it before," said Linda Calkins of Warsaw, N.Y., whose husband, James R. Calkins, joined the impromptu band of old soldiers. "It's a common bond. They were just walking up and shaking hands, and saying 'glad you're home,' that sort of thing."

The unit's four straggly rows grew longer as more veterans, hearing the tuneless cadence cry, fell in. And by the time they had reached the base of the Capitol, they were sharing the pride and purpose, as well as a peculiar guilt for having survived when death took so many friends.

"I could have been in that box as well as he could," said Burton Plamondron, who served in Vietnam as a machine gunner in 1969 and 1970. "If you've never been in a war, then I can't explain to you why I'm here any better than that."

At the foot of the Hill, they were told they would not be allowed to be part of the parade. "Betcha that dog gets to march in the parade," was the angry reaction of one veteran, pointing to one of the police force's German shepherds.

Police took two self-appointed leaders to the military authorities, and after disappearing up the Hill in a police car, the two men returned with the news that well, they would be permitted to bring up the rear.

"We'll be bringing up the rear, but we're always bringing up the rear," shouted one of them. William Van Dyke, a burly and disheveled motorcyclist, added, "We may not be in a position of honor today, but we'll be there someday because we ain't dead yet." His prediction prompted a round of applause.

The disparate group mustered up its dormant sense of military discipline, and before long, formed a disciplined and distinguished unit. "We're here for a real purpose. Let's form ranks and look like real gentlemen, even though we may look like ragtags," exhorted one veteran, sporting an untucked blue Oxford shirt over a pair of tired blue jeans. Said another veteran: "We should try to stay in step--we really should."

They were last. They had no glittering uniforms. They had no martial music to proclaim their presence. Only the wail of a lonesome bagpiper, crying "Amazing Grace." But it was for those soldiers that people in the crowd lifted their heads, stood on their toes to better see, and applaud. Oh so softly. And in the bouts of solemn silence that followed, all that could be heard were their old army boots pounding the pavement, in perfect step.