There are a lot of classic movies I’ve never seen, but, being the fount of useless knowledge that I am, I’m surprised and delighted when I find a great movie I’ve never even heard of.

Today it was “36 Hours,” from 1965, a black-and-white movie at a time when black-and-white movies were on the way out. It stars James Garner, Rod Taylor and Eva Marie Saint in a World War II psychological spy thriller. Garner plays an American officer with knowledge of the plans for D-Day. He is kidnapped by the Germans and sent to a fake U.S. military hospital, where Taylor and Saint try to convince him that he’s had amnesia for six years and the war is long since over.

Taylor’s character is supposed to have been born in the U.S., and because of what he’s trying to do he must speak completely in an American accent and idiom. He’s clever, energetic, and he must do battle with an oafish SS agent (played by Werner Peters, an almost dead ringer for Dana Elcar from “MacGyver” and “The Sting”) who wants to use his own methods to extract information from Garner. All of that makes Taylor’s character seem almost sympathetic until you stop and remember for whom he’s working.

Garner, meanwhile, gives his usual terrific performance, as does Saint.

I thought after reading a synopsis that I knew which direction the story might go. I was quite wrong. I shouldn’t be surprised by that, since the movie is based on a story by the late Roald Dahl of “Charlie and the Chocolate Factory” fame. This is no children’s story, of course.

There are a few improbabilities, but the basic story is so compelling that nobody should mind.

If you see this movie (and I recommend it, obviously), look for John Banner, Sgt. Schultz from “Hogan’s Heroes,” in a small but pivotal role.

The movie will be released on DVD this summer. Or you can try adding it to your TiVo wish list in case TCM runs it again.