Amazon’s Prime Video is a lot like Netflix: Both of the video streaming services have a lot of old TV shows, some old movies and some new stuff the companies make themselves.

Now Amazon gets to boast that it has something Netflix doesn’t have: The ability to let users download some TV shows and movies to their phones and tablets so they can watch them later, without an Internet connection.

Amazon has already offered that feature for a couple of years, but only for its own Fire tablets. Now it’s making a big leap forward by offering the capability for iPhones, iPads and Android devices.

It’s not the kind of thing you’ll want to do all the time, because Wi-Fi connections are pretty plentiful these days. But when you want it — like when you’re getting on a cross-country flight — you may really like it. You might even tell a friend.

The feature isn’t available for every video Amazon streams, since Amazon needs to work out deals with individual content owners (that is, pay them more money). Amazon says it has “thousands” of titles available for download; in most cases, subscribers will have 15 to 30 days to watch them.

And it looks like those titles include a pretty diverse lineup: There are Amazon’s own home-grown shows, like “Transparent,” of course. But there are also offerings from CBS (“The Good Wife”), Fox (“Sons of Anarchy”), Lionsgate (“The Hunger Games”) and Paramount (“Star Trek Into Darkness”). (Correction: An earlier version of this story incorrectly attributed “The Hunger Games” to MGM).)

One particularly noteworthy get: Amazon says Prime members can download the old HBO shows that Amazon landed last year, including “Girls,” “Entourage” and “The Wire.” That’s something even HBO and HBO Now subscribers can’t do.

Prime Video is one of several features Amazon has jammed into its $99-a-year Prime shipping service, and it doesn’t appear to have anything like the usage that Netflix does, based on anecdotal reports from video executives as well as bandwidth analysis from Sandvine.

But Amazon’s overriding goal isn’t to beat Netflix — it’s to get more people to sign up for Prime, and to keep the ones who sign on. This move seems like it might help those goals.