A two-tube shock absorber for automotive vehicles is furnished with a shock absorber valve positioned at the lower end of its power cylinder and comprising a pilot control stage, a main stage to adjust its "soft" characteristic curve which is desired for reasons of driving comfort, or a special characteristic curve out of a field of potential characteristic curves. According to the invention, in a lower range of piston speed the shock absorbing power is determined exclusively by the variable cross-sectional area of flow of the pilot control stage wherein the main stage remains closed. In an upper range of piston speed the shock absorbing power is determined by the variable flow cross-sectional areas both of the main stage and of the pilot control stage.