DALLAS – Blockbuster Inc., the nation’s biggest movie rental company, says it will eliminate late fees on games and movies as of Jan. 1 – but if you keep them too long, you buy them.

Blockbuster announced Tuesday it will continue to set due dates, with one week for games and two days or one week for movies, but will give customers a one-week grace period at no additional charge, beginning New Year’s Day.

“Doing away with late fees is the biggest and most important customer benefit we’ve ever offered in our company’s history,” John Antioco, Blockbuster Inc. chairman and chief executive, said in a prepared statement. “So as of the first of the year, if our customers need an extra day or two with their movies and games, they can take it.”

However, renters who keep the movies or games past the grace period will automatically be charged for purchasing the DVD or tape, minus the rental fee, Blockbuster said.

Customers will still be allowed to return the movie or game over the next 30 days for a refund of the purchase price, but will be charged a “minimal” restocking fee, the company said.

Blockbuster, facing competition from Internet-based NetFlix and movie-on-demand offerings from cable operators, said it has tested the program in some markets and found that increased rentals and retail sales offset the decline in revenue resulting from eliminating late fees.