In a method of operating a compressor near the compressor pumping limit wherein the compressor includes a control arrangement for adjusting the momentary operating state of the compressor, the flow velocity of a mass flow through the compressor in the boundary layer along the wall of the flow passage is determined for detecting operation of the compressor close to the pumping limit from a reversal of the direction of the mass flow vector in the boundary layer and the control arrangement is actuated so as to prevent the compressor from transgressing the pumping limit.