The apparatus includes at least one membrane filter (32) for filtering a machining liquid which has been contaminated by its use in electroerosive or electrochemical machining of workpieces. The apparatus also includes a device for cyclical cleaning of the soiled membrane filter, which device irradiates the membrane filter (32) with ultrasonic waves (33) and loosens the contaminant particles in the filter pores as well as means (20, 23, 24, 25, 35, 36, 41) for the backwashing of the membrane filter and for removal of the contaminant particles. The contaminant particles are fed by means of throughflushing intervals from the concentrate chamber (30) into the sedementation vessel (12). As a result of this combination of ultrasound and backwashing, extremely small durations of the cleaning cycles and uniform cleaning of the complete filter area are insured without concern for the nonuniform contaminants topography of the filter surface resulting from the contaminants.