In the cylindrical grinding of the main and rod bearings of crankshafts, the rod bearings are ground prior to the main bearings. The advantage of this is that the deformations that unavoidably occur, mainly during grinding of the rod bearings due to the removal of ground material are taken into account and compensated for again during grinding of the main bearings. The rod bearings are ground through CNC-control in the pin-chasing grinding method, and the crankshaft is held in a rotating axis in the process, said axis defined by two bearing points in the longitudinal extension of the crankshaft main bearing which are only machined. Deviations in said actual rotating axis from the determining geometric longitudinal axis of the crankshaft are taken into account in the pin-chasing grinding method by the computer of the grinding machine. The finished ground rod bearings then have an exact relation to the main bearings, which would have been ground strictly according to the determining geometric longitudinal axis of the crankshaft.