A turbomachine with at least one rotor (6), no or at least one stator (7), and a casing (1), with the rotor (6) comprising several rotor blades (8) attached to a rotating shaft, and with the stator (7) being provided with stationary stator blades (9). The casing (1) is passed by a fluid flowing through rotor (6) and stator (7), and means for the supply of fluid are provided on at least one blade (8, 9) of a blade row of the rotor (6) and/or the stator (7) on aerodynamically critical locations on trailing edge and rim-near surfaces (HRO).