A grinding machine comprises two rotary tool spindles 4, 6, each able to carry at least two grinding wheels 20,22,24, and a transfer mechanism (40,64 figure 4a), preferably comprising clamping mechanisms (40,64 figure 4a), operable to transfer a grinding wheel 22 mounted on one of the tool spindles onto the other tool spindle. Preferably there are three grinding wheels, of which one can be transferred from one grinding tool spindle to the other by the transfer mechanism. Also disclosed is a grinding wheel 20 with a central opening (50, figure 4a) and a circumferentially extending groove (52, figure 4a) which can be engaged by a clamp mechanism (40, figure 4a) preferably where the groove comprises opposing sidewall faces (54, 56, figure 4a)
