The development is the latest in a flurry of new streaming services from media, telecom and technology companies that are trying to keep pace with the digital competitors Netflix, Amazon and Hulu and stay relevant to a generation of viewers who pay for Internet access but not traditional TV subscriptions. In April, HBO started its new $15 digital streaming service called HBO Now. Showtime’s owner, the CBS Corporation, introduced an Internet-only subscription offering last year.

The new services offer viewers more flexibility to choose which programming they want to pay for and how they want to watch it. Dish Network, for instance, offers a $20-a-month service with about 20 channels in the core package and extra add-on packages for $5 a month. Apple also is in talks to include broadcast networks in a new streaming service.

“Across CBS, we are constantly finding new ways to monetize our programming by capitalizing on opportunities presented by technology,” Leslie Moonves, chief executive of CBS, said in a statement.

While HBO has said that its target is the 10 million homes in the United States that have Internet service but no traditional cable or satellite television subscriptions, Showtime’s aim is much broader. Showtime now counts nearly 24 million subscribers, and is seeking to greatly expand its base with the new service.