Abstract: The invention relates to a machine (1) for grinding the blades of a turbine rotor (2) or a compressor. The inventive machine consists of a rotary head (6) which is provided with two different grinding wheels (7, 7?) for grinding the rotors (2), three carriages (8, 9, 10) of the head which are used for the linear and angular movement thereof, a machine control unit (16) comprising a numerical control (CNC) which is used to calculate the grinding position of each grinding wheel, an optical sensor (19) which is used to measure the radius R of the blades and a device (12, 13) for the individual shaping of each grinding wheel which is supported on a carriage (14, 15) with means for the linear movement thereof (U, C) and which operates automatically during the grinding process without altering the position of the grinding wheel.