A vane compressor includes a hollow stator, and a rotor which is received in the stator for rotation about an axis. The rotor is provided with a plurality of throughgoing passages which extend radially and outwardly relative to the axis. Each passage receives a vane which has an outer end face directed towards an inner circumference of the stator and an inner end face directed away from the inner circumference of the stator. The vanes are shiftable radially in the respective passages relative to the axis. A pressure medium is supplied under a first pressure to the inner end faces of the vanes to urge the same radially outwardly for engagement of the outer end faces with the inner circumference of the stator. When the rotor is rotated, the vanes are subjected to an additional second pressure resulting from centrifugal force. The second pressure additionally urges the vanes against the inner circumference of the stator. The first and second pressures together constitute a cumulative force which above a predetermined level causes undesired frictional losses at the interfaces between the outer end faces of the vanes and the inner circumference of the stator. An arrangement is provided to decrease the cumulative pressure to the predetermined level to thereby eliminate the undesired frictional losses.