Jeannette Elmslie, 81, has been voting for years at the Cleveland Park Library, but when she went there yesterday to make sure she was properly listed on one of the registration rolls made public by the elections board, she couldn't find her name.

"I devoted this whole day to coming down here," she said to a harassed librarian struggling with three thick computer printouts of voter lists. "I'm in my 82nd year . . . [My husband] is in Arlington Cemetery and pretty soon I'll be with him. I shouldn't have to go through all this."

Around the city yesterday, anxious voters like Elmslie turned up to see for themselves whether their names appeared on voter rolls posted by the elections board at the city's 23 public libraries. Cards were provided for voters to fill out if they couldn't find their names, and many did so. Many others, however, were turned away early in the day because the lists were late in being delivered to the libraries.

Election officials said the process of name checking is vital if registration lists are to be cleaned up in the wake of the enormous snafu in which 20,000 voters had to vote special challenged ballots in the Sept. 14 primary.

The Martin Luther King Library downtown has a complete citywide voter list, while branch libraries have the rolls only for the precincts in their area. The rolls will remain in the libraries until the election, and cards filled out by voters who find problems will form a supplemental registration list that officials said would be at the polls election day.

While voters struggled with the lists yesterday, acting elections board executive director David Splitt told 175 poll workers in two training sessions that anyone who shows up at a polling place Nov. 2 with reasonable proof of residence in the ward should be allowed to vote.

"Believe me, we're bending over backwards" to make sure every qualified voter is allowed to vote, Splitt told 100 Ward 4 poll workers in the auditorium of Whittier Elementary School at Fifth and Sheridan streets NW.

Splitt told the group that precinct captains -- the citizens hired by the election board to run the 137 precincts on election day -- will have more authority than ever before to allow people to vote in the coming election.

He said anyone may vote "if the precinct captain is satisfied" that the person lives in the precinct and is a registered voter.

Persons whose names appear on the computer lists at precincts or who have voter registration cards simply will cast a ballot, Splitt said. Those who do not appear on the lists or have cards will have to show some other proof of residence and sign an affidavit swearing that they are a registered voter and then can vote a regular ballot.

Proof of residence could be a driver's license or even a friend or spouse present who is clearly a registered voter and who affirms verbally thatthe person is a registered voter in the ward.

People who don't have any proof of residency still may cast challenged ballots, which would be checked against master registration lists before being counted, Splitt said.

Yesterday, hundreds of voters showed up to check their names, and a good deal of confusion was reported at 10 libraries checked by reporters. At the Southwest branch library at Wesley Place and K Street SW, area residents were waiting to see the rolls when the doors opened -- but the lists weren't there yet.

"People were kind of disappointed," said Janelle Turner, a librarian at the Capitol View library on Central Avenue SE, where lists arrived at about 3:30. She said residents began calling about the lists as early as Monday afternoon.

Splitt said the board had expected the library system to distribute the lists, then moved at the last minute to take over the task itself when officials learned that the library distribution could delay the arrival of some lists until Wednesday.

At the Georgetown regional branch, voters complained that they could not easily find their name on the lists unless they knew their precinct, since the names on the lists were divided alphabetically by precinct. In those cases, the librarians had to look up the voter's address in a reference book to determine the precinct.

"I haven't been able to get anything else done today," said June Sweeney, the regional librarian at Georgetown branch.

Back at Cleveland Park, librarian Yeme Tucker finally found Elmslie's name -- under an old address and on the wrong precinct list. Elmslie filled out a correction card, and Tucker offered a little reassurance. "You're all clear," the librarian said. "You still come here to vote."