Semiconductor material substrates are polished by a method including at least one polishing step A by means of which the substrate is polished on a polishing pad containing an abrasive material bonded in the polishing pad and a polishing agent solution is introduced between the substrate and the polishing pad during the polishing step; and at least one polishing step B by means of which the substrate is polished on a polishing pad containing an abrasive material-containing polishing pad and wherein a polishing agent slurry containing unbonded abrasive material is introduced between the substrate and the polishing pad during the polishing step.