The invention relates to a method and a grinding machine for grinding short and/or bar-shaped workpieces, by means of which complete processing of workpieces is possible at very short cycle times by grinding two parallel end faces and the outside contour of the side faces. The grinding machine has two grinding spindles having parallel rotational axes disposed on a common grinding spindle head in a tandem arrangement and advanced together in the X direction. In coordination with a special holding and transport fixture for the workpieces, two workpieces are each ground at the same time at leastin segments, wherein the end faces of one workpiece are ground in one processing position and the final non-circular grinding of the outer contour of a second workpieces occurs in a second processingstation, the end faces thereof having been previously finish ground.