Abstract: In a process for finishing the hardened teeth of a bevel gear wheel by grinding after hardening, the ground teeth are fine- honed, this procedure being carried out in the same chucking as the preceding grinding. A machine especially suitable for this procedure has a chucking device for the bevel gear wheel (12) and a double machining head for mounting two machining tools, namely a grinding wheel (26) and a honing wheel (28). The bevel gear wheel (12) to be machined is preferably a pinion, and accordingly the honing wheel (28) is a bevel gear-type machining tool. Pairing the ground and honed pinion (12) with a bevel gear which has been only ground results in a good noise standard, and the lapping required for hypoid gears manufactured in the traditional way, with its associated drawbacks, is unnecessary.