Abstract: The method for damping global flow oscillations (20a.x, 20b.x) in a flowing medium in the region of an unstable flow (10) separating itself from at least one boundary surface (11, 12) is comprised of detecting the global flow oscillations with a sensor system (13) and superimposing a compensatory oscillation (15, 16) controlled by the signals of the sensor system onto the flowing medium in a separation zone of the separated unstable flow. Correspondingly, the apparatus for performing the method comprises a generator (17, 18) which superimposes a compensatory oscillation on the flowing medium in a separation zone of the separated unstable flow and a control system (28, 29) which evaluates the signals of the sensor system and controls the compensatory oscillation so that the amplitude of the global flow oscillation is damped by a prespecified factor.