Mark Twain once described the public library as “the most enduring of memorials,” a free center of intellectual and educational power accessible to old and young alike. Libraries today are seeking to keep it that way, with many offering a reprieve to those who fail to return their books on time.

Last week, the Free Library of Philadelphia ended its policy of charging fines on overdue materials. It is one of several library systems, among them Los Angeles, Chicago, Denver and San Diego, that have adopted a no-fee or amnesty policy in recent years.

In Philadelphia, lost or destroyed items need to be replaced before people can check out more books, said Siobhan A. Reardon, the director of the Free Library. However, in lieu of cash, the library also accepts “new or gently used copies” as replacements. Why? Libraries want the books and other materials back so other patrons can enjoy them, too.

“We watched other libraries go down this path with success,” Ms. Reardon said in an interview. The new policy, she added, encourages people to keep coming to the library without absolving violators of their responsibility. “You can’t get another book until you return the one you have,” she said.