Abstract: A grinding machine, in particular a face grinder for grinding the faces of silicon wafers, has a grinding wheel spindle (20) and a work spindle (22) which are mounted so as to be pivotal about axes (A and B) respectively, each axis being perpendicular to the rotational axis of its respective spindle and being orthogonal to the rotation axis of the other spindle. Three sensors or probes (1 to 3) are provided to measure the position of one spindle relative to the other and to generate signals for controlling servo motors (26, 28) for adjusting the angular orientation of each spindle about its pivotal axis.