A hydromechanical driving device generates forward-pushing movements of a band-shaped filter material according to the pressure prevailing in the fluid to be filtered to operate band filter devices. The hydromechanical driving device includes a hydraulic accumulator (29) provided with a movable element (31) separating a first storage space (33) from a second storage space (35). The side of the separating element (31) bordering the first storage space (33) is impinged upon by the pressure generated the first storage space by the fluid to be filtered. A mechanical device (17) translates a movement of the separating element (31) into a forward pushing movement. A pressure control unit (47, 49, 51) generates lower pressure in the second storage space (35) than the pressure generated by the fluid to be filtered according to the amount of pressure and/or the degree of impurity of the fluid to be filtered. The lower pressure causes the separating element to be displaced.