From the second-floor balcony at the Brooklyn Public Library, Jundallah Smith, 17, and Ricardo Leriche, 19, eyed a tete-a-tete in the lobby.

''She's talking to him?'' Jundallah said, incredulously.

The two young men had come to the library's central facility, at Grand Army Plaza, less to study than to socialize, as they do most afternoons.

''There's not much in my school in the way of after-school activities,'' said Jundallah, who attends Sarah J. Hale High School. And the library, patrolled by peace officers, is safe. ''You get in trouble on the streets,'' Ricardo said. Besides, he added, ''You can meet girls.''

The two young men have plenty of company at their favorite afternoon destination. Between 3 P.M. and 6 P.M., the library swarms with children and teen-agers. For many, it is a pastime by default. ''There's nothing else to do,'' said Matthew Rogers, 10, who comes daily with his 9-year-old best friend and then walks home at 6 P.M.

As policy makers bemoan the lack of after-school options for young people, libraries remain a little-noticed catchment, one that is free, open to all and safe in the eyes of parents and children.

But acting as a de facto day-care center occasionally overburdens this Brooklyn facility, and sometimes creates tension among competing constituents. ''Adults who come in are often completely turned off and leave,'' one librarian said. ''The city should provide some place for these kids to go.''

Some middle-class parents from Park Slope, which abuts the library on the west, say they find parts of the library increasingly inhospitable after school. ''It's started to become really unmanageable in the children's room,'' said Ellen Shea, a Park Slope parent. After school, she said, ''There are no books left and if you read to your kids they can't hear you.''

But Ms. Shea said she was sympathetic to the plight of parents who have no other options, particularly as financing cuts have eviscerated affordable after-school programs. One such mother is Susan George, who makes her living as a baby sitter and lives in Crown Heights, which extends east from Grand Army Plaza.

When her children, now 14 and 16, were much smaller, she said, she frequently sent them to the library after school, then would pick them up on her way home from work. She did not want her children home alone, and after-school programs were always full. At the library, she said, ''They were really, really safe.''

The library's peace officers often act as guardians and disciplinarians, given that harried reference librarians do not have the time. ''They need a safe haven,'' said Philip Mastridge, the central library's operations lieutenant. ''We try to provide it.''

His officers' biggest problem, he said, is the large number of toddlers who are accompanied only by a sibling, usually under 13. As often as two or three times a day, he said, patrons bring toddlers who have wandered off or been forgotten by older siblings to the security desk.

Brian Kenney, a division manager at the central library, said it had long been a home for latchkey children, although the situation seems to have worsened in recent years. Where possible, he said, the library provides activities to get children ''off the floor,'' though such programs are limited by a lack of staff and space. And he said that the library will soon undergo a major renovation that will create more quiet areas.

In the end, however, young people are the library's customers, too, Mr. Kenney said.

Technology, particularly computers installed in 1996, attract teen-agers who might otherwise shun the library, he noted, and that is a trend to be welcomed.

''No librarian,'' he said, ''would rather not have kids.'' AMY WALDMAN

Photo: The children's room at Brooklyn's central library is packed after school. (Marilynn K. Yee/The New York Times)