A passive damping system for a shock absorber is disclosed. The shock absorber includes a working chamber, and a piston disposed in the working chamber. The piston includes a primary bypass valve for defining an upper fluid portion and a lower fluid portion. A piston rod is connected to the piston and extends through the top portion of the working chamber. A variable bypass assembly is disposed between a first fluid chamber and a second fluid chamber. The variable bypass assembly includes at least one bypass aperture for providing communication of damping fluid between the first and second fluid chambers. The variable bypass assembly also includes a passive control member for varying the size of the bypass aperture, and biasing structure for normally retaining the passive control member in a position which maximizes the size of the bypass aperture. The passive control member is such that an accelerating force placed upon the shock absorber causes motion of the passive control member for restricting the size of the bypass aperture and increasing a damping force provided by the shock absorber.