Thousands of Vietnam veterans from across America marched in a grand parade down Washington's Constitution Avenue yesterday, then gathered in a vast throng on the Mall to dedicate the National Vietnam Veterans Memorial, on whose polished granite walls are etched the names of their 57,939 dead and missing comrades-in-arms.

It was a day of flags and tears and stirring music, of marching Green Berets in jungle fatigues and Gold Star Mothers in cream-colored capes. There were military color guards and high school bands playing "The Girl I Left Behind Me" and "God Bless America"; and, at noon, from an overflight of military aircraft, the roar of jet warplanes and the haunting thud of rotor blades.

"All of us can now say we are proud to be Vietnam veterans . . . and I know that our country appreciates our service," Jan C. Scruggs said at the dedication ceremony. Scruggs is the wounded former specialist 4 whose dream it was to build the memorial and who headed the group that did so. "Today we see this dream is a reality . . . . Let it begin the healing process and forever stand as a symbol of our national unity."

Some 150,000 attended the parade and dedication despite gusty winds and temperatures in the 40s, according to a National Park Service estimate. The day's events capped a week of activities in what Scruggs and his group planned as a long-overdue "National Salute to Vietnam Veterans." Fifteen thousand veterans, many in faded uniforms, marched in the parade in ranks arranged by states and territories.

The parade's theme was "Marching Along Together Again." While there were tears at some of the music and memories, there were also cheers and applause from a crowd along the parade route that seemed to surge with patriotism. They waved small American flags, and many brought their children, bundled tightly against the wind.

Many spectators said they had no direct involvement in the Vietnam War but came to pay tribute to those who fought an unpopular war. "I felt like I owe it to the people who served," said Jim Peebles, a 26-year-old graduate student at George Washington University. "I was one of those who was not too appreciative . . . . I'm sure I contributed to the national disavowal. My being here is saying, 'I'm sorry for the way America was.' "

One woman along the route of the three-hour parade held up a sign that said simply, "Thanks!"

Many veterans and their families and friends -- the bulk of the crowd -- felt it was time for the apology. "It's about time we were recognized," said William Wagner, 31, of New Jersey, who was a Navy petty officer 1st class in Vietnam from 1970 to 1973. "It's about time the men who gave their lives and the men sitting in VA hospitals were recognized. My reason for being here is for the ones who can't be here. I had a lot of buddies get killed over there."

"They should have had this when we first came back in 1971," said Ben Lucero, who flew here from New Mexico for the parade and dedication and who was an Army staff sergeant in Vietnam. "It's just beautiful."

Retired Gen. William C. Westmoreland, commander of American forces in Vietnam from 1964 to 1968, marched with the Alabama contingent of veterans at the head of the morning parade. He carried two small American flags.

Later, just before the dedication of the memorial, Westmoreland, wearing a trench coat and a button that said, "I'm proud to be a Vietnam veteran," viewed a mockup of the statue of the three Vietnam GIs that eventually will be erected near the V-shaped granite memorial, saying he was glad the statue will be added.

Maya Lin, whose design for the memorial won a national competition and set off a fierce controversy that resulted in the decision to add the statue and an American flag, stood on the reviewing stand at yesterday morning's parade, holding a small American flag and occasionally smiling as the veterans marched by. She attended the dedication but was not recognized as part of the official program.

The dedication ceremony was marked by the uplifting rhetoric of national veterans' leaders and of those who struggled for three years to build the memorial.

"Today we dedicate a memorial to a generation of Americans who fought a lonely battle," said Al Keller Jr., national commander of the American Legion. He said the legacy of America's experience in Vietnam is "the rediscovery of our capacity to care, to give, and to honor . . . . This memorial symbolizes not only the supreme gift of 57,939 young Americans, but also the priceless gift of renewed awareness of our capacity as a people."

A letter from Defense Secretary Casper Weinberger to Scruggs, read at the ceremony, said: "When your country called, you came. When your country refused you honor, you remained silent. With time, our nation's wounds have healed. We have finally come to appreciate your sacrifices and to pay you your tribute you so richly deserve."

Billy Ray Cameron, a Vietnam veteran and the junior commander-in-chief of the Veterans of Foreign Wars, echoed the theme of reconciliation. "To me," he said, "this memorial has served its highest purpose: to reunite our beloved America with her bravest and best . . . . "

Helen J. Stuber, who lost her son Dan in Vietnam, and who is now the national president of American Gold Star Mothers, said simply, "I am so grateful after all these years that our country is pausing to honor the Vietnam veterans in this our nation's capital for the welcome home they never received.

"In the heart of mothers," she added, "the hurt will never go away. However, we would rather forget the sad tears and remember the happy memories of our children."

John Wheeler, a Vietnam veteran and chairman of the Vietnam Veterans Memorial Fund, said the memorial is another gift to America from those who died in the war. "America affirms the integrity of her fighting forces without apology or stain," said Wheeler. " . . . The veterans who returned from Vietnam have much to offer our country in all walks of life."

The speeches were made from a platform high above the apex of the memorial, and the tightly packed crowd stretched from below the platform far into the distance toward the Washington Monument on the east and the Lincoln Memorial, closer at hand to the west.

The only visible sign of protest came from a group called the Black Veterans For Social Justice, whose members held their own parade and counterdemonstration on a hill overlooking Constitution Avenue.

About a dozen members of the group planted a red, black and green flag in the grass and taunted the crowd and speakers with loud boos.

The group's spokesman, who identified himself as Brother Jay Jones, noted what he called the conspicuous absence of many black veterans from the week's observances. "When they speak of Vietnam vets, the black man is not included," he said. "We want to bring the black perspective on this march. More black and Third World people fought on the front line in Vietnam than in any other war. But the sons of rich white people hauled ass to Canada, and now they've been pardoned, and that shows me I was a fool."

Behind the speaker's stage, a group of about 25 Vietnamese men and women unfurled a dozen large Vietnamese flags, yellow with three red stripes. One member of the group wore a sign on his back that read: "Freedom and Justice Are What Vietnam Vets Fought For."

A spokesman identified the group as the National Front For the Liberation of Vietnam. He said they were invited by a local American Legion post to come down and show their support for America's Vietnam veterans.

Sitting near the edge of the speakers' stage was 86-year-old Joseph Ambrose of Joliet, Ill. Ambrose, a World War I veteran, wore his battered doughboy's uniform. Over his shoulder was slung his World War I canteen, shoulder bag, and his extra boots, with holes in the toes. He carried a tattered American flag, which had been draped over the casket of his son Clement, who was killed in the Korean War.

Ambrose, who now wears a hearing aid, handed out statements calling the Korean conflict "the first war we could not win conclusively and it was one we therefore would just as soon forget . . . . It may be that in years to come we will remember both Vietnam and Korea with pride."

But the day belonged to the veterans of America's most recent war:

To the American Indians from North and South Dakota and California, who marched in the veterans' parade wearing traditional Indian feathered headdresses and their combat uniforms. "We're a bunch of redskins," said Rick McLaughlin, who held a homemade staff with the colors of the American Gold Star Mothers, decorated with two feathers "to symbolize the two worlds America and Vietnam we were in."

To the 70 who came from faraway Oregon after a successful veterans fund-raiser netted $24,000 for their trip. "We've finally come home from Southeast Asia to be here," said Marine Mike Conner. "We're come 10,000 miles from Vietnam to be here. This is the end of a dream."

To Bill Ward, in the Army in Vietnam from 1966 to 1967, who shook off the chilly, gusty winds, saying: "I'd stand in the snow to be out here."

To Bob Wieland, 36, a veteran who lost both legs above the knees in Vietnam 13 years ago and who recently began walking from California to Washington to publicize the veterans' plight. Wieland said he interrupted his walk in the middle of the California desert to come here. When it's over, he will pick up where he left off. "This means a lot to me," he said. "This is fantastic. The unity among Vietnam veterans is incredible."

And to Dennis D'Andrea, who served in an Army airborne division from 1966 to 1969. "We waited 15 years to get here, man," he said. "But it's not too late. I'm just proud I can be here. We made it. It's just like coming home, man."