A surge arrester module comprising: - a first end electrode and a second end electrode spaced apart in the axial direction of the surge arrester module; - a stack of cylindrical elements arranged between the first and second end electrodes (2, 3), at least one of these cylindrical elements being a varistor block; and - an outer casing of electrically insulating material, characterized in: - that the first end electrode comprises a first part of electrically conductive material and an adjacent second part of electrically conductive material, the first part being located between the second part and said stack and being provided with a first contact surface configured to abut against a corresponding second contact surface of the second part; - that an electrical connecting element is provided between the first and second parts (7, 8) of the first end electrode, the electrical connecting element being configured to keep these parts (7, 8) electrically connected to each other in case of the formation of a gap between said first and second contact surfaces (9, 10); - that at least one clamping member (12; 112) of electrically insulating material is connected to the second end electrode and to the first part of the first end electrode and configured to press the second end electrode and the first part of the first end electrode towards each other in the axial direction of the surge arrester module to thereby achieve contact pressure between the cylindrical elements of said stack and clamp the stack between the second end electrode and the first part of the first end electrode; and - that said at least one clamping member or at least one other clamping member of electrically insulating material is connected to the second end electrode and to the second part of the first end electrode and configured to press the second end electrode and the second part of the first end electrode towards each other in the axial direction of the surge arrester module to thereby achieve contact pressure between said first and second contact surfaces (9, 10). - a first end electrode and a second end electrode spaced apart in the axial direction of the surge arrester module; - a stack of cylindrical elements arranged between the first and second end electrodes (2, 3), at least one of these cylindrical elements being a varistor block; and - an outer casing of electrically insulating material, - that the first end electrode comprises a first part of electrically conductive material and an adjacent second part of electrically conductive material, the first part being located between the second part and said stack and being provided with a first contact surface configured to abut against a corresponding second contact surface of the second part; - that an electrical connecting element is provided between the first and second parts (7, 8) of the first end electrode, the electrical connecting element being configured to keep these parts (7, 8) electrically connected to each other in case of the formation of a gap between said first and second contact surfaces (9, 10); - that at least one clamping member (12; 112) of electrically insulating material is connected to the second end electrode and to the first part of the first end electrode and configured to press the second end electrode and the first part of the first end electrode towards each other in the axial direction of the surge arrester module to thereby achieve contact pressure between the cylindrical elements of said stack and clamp the stack between the second end electrode and the first part of the first end electrode; and - that said at least one clamping member or at least one other clamping member of electrically insulating material is connected to the second end electrode and to the second part of the first end electrode and configured to press the second end electrode and the second part of the first end electrode towards each other in the axial direction of the surge arrester module to thereby achieve contact pressure between said first and second contact surfaces (9, 10).