Abstract: In a first step for the purpose of precentering, the dressing too; (27), without axial movement, is brought into contact with the circumference of the rotating grinding worm (11), and those rotary-angle positions of the grinding worm (11) at which the overrunning of the thread gap (36) starts of ends are determined by means of an acoustic-sensor signal and the shaft-angle encoder (18) of the grinding spindle (16). In a second step for the purpose of precision centering, the dressing tool (27) fed into the thread gap (36) is brought into contact with the left-hand and right-hand tooth flanks (38, 39) by axial displacement. In this case, the axial infeed is stopped by means of the acoustic-sensor signal, and the exact grinding-worm thread center is calculated from the contact positions of the dressing tool (27) achieved.