A gripper system for a machine that processes printing material sheets has a gripper with a first clamping surface and a gripper pad, for cooperating with the gripper, with a second clamping surface. One of the two clamping surfaces is formed with a surface relief. The clamping surface which has the surface relief is placed in such a way that, when a narrow printing material sheet is gripped, the clamping surface is covered by the sheet only within a subregion of the clamping surface and, when it grips a broad printing material sheet, it is covered by the latter beyond the subregion. The surface relief is structured differently within the subregion than outside the subregion, in that it is provided within the subregion with an antideformation structure which protects the narrow printing material sheet from excessive clamping deformation.