Comcast Corp. said Monday it will be streaming HBO and Cinemax shows, movies and other content online to 5,000 subscriber households in a national trial set to start in coming weeks. It is the first time the two premium movie channels will be offering their programs over the Internet to computers. Downloads to mobile devices may come in the future.

HBO and Cinemax will join TNT, TBS and Starz in Comcast’s online video trial. If the technical test is successful, Comcast will roll out access coast-to-coast to its subscribers at no additional cost.

The trial is part of a joint effort with Time Warner Inc. to offer cable programming on the Internet as viewership increasingly moves outside of the living room. But programmers and pay-TV operators will provide access only behind a walled garden of subscribers.

Unveiled last month, the venture dubbed “TV Everywhere” by Time Warner and “On Demand Online” by Comcast began with TNT and TBS.