The music video directed by Anton Corbijn features all of the band members holding babies. In the beginning of the music video, Alan Wilder is shown on a porch waiting for something. A man dressed almost like a daredevil rides a motorcycle with a baby. He drives to Alan on the porch and hands him the baby. The video shows the other members of the band holding a baby. One baby grabs onto Martin’s hair and yanks it profusely while he smiles.

The music video for A Question of Time is the first DM video to be directed by Anton Corbijn, and was the start of a relationship with him and the band which still lasts to this day. It was included on the Strange video, The Videos 86-98, the DVD of The Best of Depeche Mode Volume 1 and on Video Singles Collection.