Power semiconductor module, comprising - at least two semiconductor chips (3, 3') and at least two first and two second base plates (4, 4', 5, 5'), which at least two semiconductor chips (3, 3') each have a first main electrode side and a second main electrode side which is situated opposite the first main electrode side, wherein the respective first base plate (4, 4') makes thermal and electrical contact with the first main electrode side in each case, and the respective second base plate (5, 5') makes thermal and electrical contact with the second main electrode side in each case, - a first cooling apparatus having at least two first main electrode connection elements and a heat sink, wherein that side of a first base plate which is averted from the first main electrode side makes thermal and electrical contact with a first main electrode connection element in each case, and wherein that side of the first main electrode connection element which is averted from the first main electrode side makes thermal contact with the heat sink in each case, - a second cooling apparatus, that side of the respective second base plates which is averted from the second main electrode side making thermal contact with the said second cooling apparatus, wherein the second cooling apparatus has at least two second main electrode connection elements, wherein that side of a second base plate which is averted from the second main electrode side makes thermal and electrical contact with a second main electrode connection element in each case, wherein the respective second main electrode connection elements make electrical contact with one another or the respective second main electrode connection elements are in the form of a common second main electrode connection element, and wherein the power semiconductor module comprises a housing in which the at least two semiconductor chips (3, 3') and the first and the second cooling apparatus (6, 7) are arranged, and wherein the heat sink of the first cooling apparatus, on that side which is situated opposite the first main electrode connection elements, is supported against the housing. - at least two semiconductor chips (3, 3') and at least two first and two second base plates (4, 4', 5, 5'), which at least two semiconductor chips (3, 3') each have a first main electrode side and a second main electrode side which is situated opposite the first main electrode side, wherein the respective first base plate (4, 4') makes thermal and electrical contact with the first main electrode side in each case, and the respective second base plate (5, 5') makes thermal and electrical contact with the second main electrode side in each case, - a first cooling apparatus having at least two first main electrode connection elements and a heat sink, wherein that side of a first base plate which is averted from the first main electrode side makes thermal and electrical contact with a first main electrode connection element in each case, and wherein that side of the first main electrode connection element which is averted from the first main electrode side makes thermal contact with the heat sink in each case, - a second cooling apparatus, that side of the respective second base plates which is averted from the second main electrode side making thermal contact with the said second cooling apparatus, wherein the second cooling apparatus has at least two second main electrode connection elements, wherein that side of a second base plate which is averted from the second main electrode side makes thermal and electrical contact with a second main electrode connection element in each case, wherein the respective second main electrode connection elements make electrical contact with one another or the respective second main electrode connection elements are in the form of a common second main electrode connection element, and wherein the power semiconductor module comprises a housing in which the at least two semiconductor chips (3, 3') and the first and the second cooling apparatus (6, 7) are arranged, and wherein the heat sink of the first cooling apparatus, on that side which is situated opposite the first main electrode connection elements, is supported against the housing.