The present invention relates to a suspension method and to a shock-absorbing device for an automobile in the broadest sense of the term, i.e. any vehicle having a suspension and moving under its own power. Said shock-absorbing device includes a damping assembly (1) having, on the inside thereof, a piston (2) connected to a rod (17), the piston (2) and the rod (17) combined therewith being movable, in both the compression and expansion direction, about a static position inside the damping assembly (1) in order to provide a shock-absorbing function, the inside of the damping assembly (1) being filled with a hydraulic fluid, characterized in that said assembly (1) engages with a means for varying the damping effect so as to produce: a compression phase consisting of a compression sub-phase, directed from the static position toward the maximum compression position of the piston (2), and of an expansion sub-phase, directed from said maximum compression position toward the static position, respectively, and an expansion phase consisting of an expansion sub-phase, directed from the static position toward the position of maximum expansion of the piston (2), and of an expansion sub-phase, directed from said maximum position toward the static position, respectively, the means for varying the damping elect controlling the damping assembly such that the damping value of the compression sub-phase of the compression phase and/or the expansion sub-phase of the expansion phase is different from the damping value of the expansion sub-phase of the compression phase and the compression sub-phase of the expansion phase, respectively. According to the invention, provided is a step of modifying the damping value with separate values for the compression direction as well as for the expansion direction for each of the work sectors of the shock absorber depending on whether the work is being carried out between the static position of the suspension and the fully compressed position, or between the static position of the suspension and the fully expanded position.