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A physical model is proposed to account for the hysteretic effects of automotive shock absorbers. Besides the oil compressibility, the compressibility of a variable gas phase in the shape of bubbles are the root of these dynamic effects. Due to the pressure dependent solubility of gas in the liquid the gas bubbles appear or disappear thus changing the compressibility characteristics. The model is used to identify the internal architecture of the damper, i.e. the valve parameters, and the hysteretic effects simultaneously. Some justifiable assumptions are introduced to estimate directly from damper force, piston displacement and velocity measurements.