RICHMOND, Va. (AP) _ Some of the estimated 35,000 people who jammed the Capitol grounds for Gov. L. Douglas Wilder's inauguration couldn't see the ceremony and had to strain to hear the oath of office. But it didn't matter.

They got what they came for: a feeling of being a part of history, seeing the nation's first elected black governor take office.

''I'm a little disappointed we couldn't get any closer,'' said Lillian Wiggins of Washington, D.C. ''But the fact that I brought my grandchildren and that it's an historic occasion makes it important that we stay.''

She added, ''We'll go home and see what happened on television.''

The crowd was more than twice as large as the one that saw Wilder's predecessor, Gerald L. Baliles, take office four years ago.

As they waited for the ceremony to begin, many in the crowd commented that the weather was ideal. Temperatures were in the 30s but seemed warmer to bundled-up spectators who were jammed shoulder-to-shoulder in bright sunshine.

Security was tight, with police guarding entrances to the grounds and ushering spectators to roped-off areas. Latecomers were stuck with bad vantage points even if they had tickets for bleachers reserved for 3,500 invitees.

''We had tickets, but we showed up late and they wouldn't let us in,'' said Nolan Dawkins, a judge from Alexandria. The Dawkins children were glad they came anyway, because they got to see the parade of marching bands and military units that followed the swearing-in ceremony.

''I wanted to come because I want to tell my kids about this when I grow up,'' said Kelli Dawkins, 9. ''I want to tell them I was there to see the first black governor.''

Kelli's sense of history was lost, however, on 3-year-old sister Ashley. Asked if she knew who Doug Wilder was, Ashley replied: ''Kelli's friend.''

Rachel Wheaton didn't make the mistake Ms. Wiggins and the Dawkins family made. The Petersburg High School history teacher and 72 students staked out places front and center at 8 a.m., four hours before the ceremony.

''Some of these kids got up at 4:30 this morning,'' Ms. Wheaton said. ''Some of them asked off their weekend jobs so they could attend, and others gave up their free Saturdays because they know this is historic not only for Virginia, but for the nation.''

Savannah Williams, a cultural anthropologist from Surry, was first in line for one of about 300 available seats for a 9 a.m. prayer service at St. Paul's Episcopal Church across from the Capitol.

''I've been standing here in the cold since 7:15,'' Ms. Williams said. ''Africans first came here in 1619, and now it's 1990. I think it's important to see a person of African descent finally become a governor.''