About 25 youthful demonstrators staged a sit-in yesterday in the offices of D.C. Public Library director Hardy R. Franklin, complaining about the operation of a summer youth-employment program at the Martin Luther King library.

The four-hour sit-in on the library's fourth floor, which is normally closed to the public, ended about 2:30 p.m. after Franklin and other library officials agreed to meet today with representatives of the youths.

There were no arrests or incidents of personal injury or property damage, Franklin said. Operations of the library were not affected.

Although there were conflicting accounts about the nature of the dispute, library officials and the youths said the problems center on supervision of the youths, who work in "The Other Place," a young-adult library and audio-visual room on the third floor.

Franklin said some of the demonstrators believed that their supervisor had improperly attempted last week to take control of several media training projects and had barred several youth employes from the library.

Franklin said various library officials have met with the youths and some of their parents in an attempt to resolve the dispute, which also involves the participation of an organization called Pyramid Communications that officials said had been using library space.

Library officials said yesterday that the Pyramid group had no official relationship with the library and that it improperly was given use of space by library employes.