Semiconductor wafers are double sided polished by a method of polishing a frontside of the wafer in a first step with a polishing pad with fixed abrasive and simultaneously polishing a backside of the wafer with a polishing pad containing no abrasive, but during which an abrasive polishing agent is introduced between the polishing pad and the backside of the wafer, inverting the wafer, and then in a second step polishing the backside of the wafer with a polishing pad containing fixed abrasive and simultaneously polishing the frontside of the wafer with a polishing pad containing no fixed abrasive, a polishing agent containing abrasive being introduced between the polishing pad and the frontside of the semiconductor wafer.