Abstract: A hole grinding machine is provided which includes a frame, two displaceable grinding spindles arranged on the frame, and two chucks facing the grinding spindles for holding and moving workpieces to be machined. The chucks are fastened to rotatable chuck spindles supported by an indexing head which is rotatably supported by a shaft arranged on the frame. The shafts of the chuck spindles are arranged in the same plane and at the same distance from but on either side of the shaft of the indexing head. Between a given pair of machining operations the indexing head is rotated one-half turn so that the chucks change places in front of the grinding spindles. The indexing head is then rotated one-half turn in the opposite direction between the next pair of machining operations, so that the head reciprocates between two end positions.