Abstract: The invention concerns a process of polishing wafers, in which a silicon wafer held on a wafer support plate rotatable under a predetermined applied pressure, is polished by mechanochemical polishing in a plurality of polishing steps with an abrasive material interposed between the wafer and a polishing pad cloth applied to a polishing surface plate moved relative to the wafer support plate at a predetermined relative speed. Quality comparable to that of wafers obtainable by a prior art three-step polishing process can be obtained with a two-step wafer polishing step comprising a primary polishing step and a final polishing step. The primary polishing step is performed by setting a high polishing pressure of 300 to 700 g/cm.sup.2 and a reference relative speed of 50 to 150 m/min., and quick increase of the relative speed to 2 to 4 times and quick reduction of the polishing pressure down to 1/2 to 1/10 are caused in a final stage of the primary polishing step.