A power semiconductor module has a substrate, a power semiconductor, a connecting device, a potting body, a pressure device, external terminal elements and a housing, the substrate has an insulant body and substrate conductor tracks, wherein the power semiconductor component is arranged on one of the substrate conductor tracks and electrically connected thereto. The connecting device is a film stack having a first electrically conductive film, a second electrically conductive film, an electrically insulating film therebetween, the connecting device is covered by the potting body, the pressure device exerts pressure on the potting body with a spring, the external terminal elements are arranged on the preformed housing or connected in a positively locking manner and have a contact device to an assigned substrate conductor track.