Their faces and accents came from all over the world, 378 people, young and old, rich and poor and middle class, all gathered before the white-columned mansion at Mount Vernon.

"I welcome you not as tourists, or as visitors to a strange land, but as citizens," they were told by Muska Brzezinski, wife of President Carter's national security adviser, Zbigniew Brzezinski.

And as they raised their right hands yesterday, reciting the oath of citizenship before U.S. District Court Judge Albert V. Bryan Jr., that is what they became.

New citizens normally are sworn in as groups of 50 or fewer in U.S. courts across the nation with little fanfare and negligible ceremony. But at a time when more people than ever are seeking to come to this country, and to become a part of it, Immigration and Naturalization Service officials felt, that "the more meaningful we can make the ceremonies the better it is. The risk is that it could all become routine."

Since yesterday was the 191st anniversary of the signing of the Constitution, it seemed a particularly appropriate occasion. Similar but smaller ceremonies were also held in the Natonal Archives building and on the steps of the state capital in Richmond.

At Mount Vernon yesterday the Marine Corps Band was playing, the color guard was marching. Rep. Herbert E. Harris (D-Va.) and Sen. Harry F. Byrd Jr (I-Va.) were on hand to welcome a new corp of voters. The Daughters of the American Revolution handed out little flags and well-wishers and relatives swarmed over the lawn as some surprised tourists looked on from the outskirts of the crowd.

The gathering of new citizens was representative of America's new immigrant population. All had worked and studied and waited for months - in many cases years - for this day. Most had had to live in the United States for a minimum of five yeras, had had to learn English and the workings of the government and had to prove to one INS investigator after another that they were of "good moral character."

Their feelings about the occasion yesterday, the stories of their pasts and their hopes for the future were as diverse as the countries from which they came.

Some, like Italian-born Francesca Greco, said they had lived in the U.S. so long "I feel American already." Deepak Singh, who was born in India and wore his accustomed turban to the ceremonies yesterday, said he thought he would be "better able to serve the goals of this country as well as mine if I became a citizen."

Cesar Espinoza, originally from Ecuador, hoped that citizenship would help him in his efforts to join the Diplomats soccer team.

Victorine Mizrahi, an elderly woman who watched the ceremonies from a wheelchair, said, "I like being a citizen. I like very much." Five years ago she arrived from Cairo, but now she said, she is "just from Alexandria, Va."

Still others, like Robert John D'Sylva, who came to this country from Pakistan in 1972, said they hoped that now they could make their children citizens as well.

"This country says freedom," D'Sylva told a reporter, "and that's what I am for - my love."

All this seemed to fly over the head of 6-year-old Ira Hess, however. One of the youngest of the new citizens yesterday, the Korean-born orphan adopted by Mr. and Mrs. Frederick Hess, declined comment, preferring instead to sip his soft drink and steadily wave his new flag.