A power semiconductor module (1) with a housing (2) and at least one semiconductor chip (3, 3′) located in it is devised. At least one semiconductor chip (3, 3′) has a first main electrode side (31) and a second main electrode side (32) opposite the first main electrode side, the first main electrode side (31) making thermal and electrical contact with the first base plate (4, 4′). The first cooling device (6) makes thermal and electrical contact with the side of the first base plate (41) facing away from the first main electrode side. The second main electrode side (32) makes thermal and electrical contact with a second base plate (5, 5′). A second cooling device (7) makes thermal contact with the side of the second base plate (51) facing away from the second main electrode side. The heat sink (65) of the first cooling device is supported against the housing (2).