Abstract: A grinding spindle holder accommodates two or more grinding spindles and is mounted on, or adapted to be fitted to a feed slide of a grinding machine. The spindle holder has a stationary base part and a movable part which accommodates the grinding spindles and which can be rotatably stepped between given terminal positions by swinging the movable holder part about a shaft extending parallel with the spindle axes, for consecutive movement of the spindles to a grinding position for engagement with a workpiece in one and the same chuck position. The movable holder part can be swung by means of a working piston-cylinder device between two stop abutments located on the base part of the holder, of which stop abutments at least one can be adjusted in a manner to accurately determine the position of a relevant grinding spindle in the grinding position. The spindle holder is also provided with means for damping the swinging movement of the movable holder part towards respective stop abutments.