Nancy Reagan, "a little bit woozy" from a fall suffered Sunday night, lost her footing twice yesterday and had to be helped by President Reagan and a Secret Service agent as she was climbing down the steps of a helicopter in Santa Monica.

At the president's victory celebration late last night, the first lady looked unsteady, though smiling at the cheering crowd. She appeared to be assisted by her son Ron, while holding hands with the president as they stood on the stage at the Century Plaza in Los Angeles.

Earlier in the day, Mrs. Reagan was also assisted as she left the helicopter that was bringing the Reagans back from Solvang, Calif., where they flew to cast their ballots at the Veterans' Memorial Building. There, the first lady also slipped and appeared to lose her balance, according to photographers traveling with the presidential party.

In Los Angeles, where they spent the day while waiting for the returns to come in, the president appeared to be more concerned about Mrs. Reagan than he was about the election.

Sheila Tate, the first lady's press secretary, said in Washington last night that Mrs. Reagan told her she has "a little residual dizziness" but the swelling had subsided and she was not taking any medication. She saw White House physician Dr. Daniel Ruge about the head injury for the second day in a row, Tate said.

Besides voting, Mrs. Reagan kept to her private schedule and planned to be at the president's side during last night's election vigil, Tate added.

The first lady's fall occurred Sunday night in a Sacramento hotel where she and the president were staying on the last leg of the campaign. During the night, she became chilled and got up to get a blanket, according to Tate.

The bed in which the Reagans were sleeping was on a raised platform and in the darkness Mrs. Reagan missed her step and "took a header," as she later described it, striking the side of her head on a chair.

The president applied first aid -- some ice -- to a lump the size of an egg at Mrs. Reagan's hairline, Tate said. Monday morning Ruge, a neurologist, examined her for the first time.

"Some recommended to her that she drop off the trip yesterday in Los Angeles, but she didn't want to do that," Deputy White House press secretary Larry Speakes said yesterday in Los Angeles.

Describing Mrs. Reagan as being "a little bit woozy ever since" her fall, he also told reporters that Ruge was "keeping a watch on it."

"She said she felt a little wobbly but she mainly felt consternation that it happened," Tate said.

The White House did not report Mrs. Reagan's injury until news reports described her as appearing tired. Monday night, she telephoned Tate to tell her why she looked tired.

"I think she's really tired," Tate said, "and is looking forward to spending some time at the ranch."