A semiconductor wafer is polished, wherein in a first step, the rear side of the wafer is polished by a polishing pad comprising fixedly bonded abrasives having a grain size of 0.1-1.0 μm, while supplying a polishing agent free of solid materials having a pH of at least 11.8, and, in a second step, the front side of the semiconductor wafer is polished, wherein a polishing agent having a pH of less than 11.8 is supplied. A polishing pad for use in apparatuses for polishing semiconductor wafers, has a layer containing abrasives, a layer composed of a stiff plastic and also a compliant, non-woven layer, wherein the layers are bonded to one another by means of pressure-sensitive adhesive layers.