An extensible mathmatical model for the torque transmission property of multi-staged stiffness clutch dampers considering hysteresis characteristics was established in virtue of the hyperbolic-tangent fitting function,which was then validated by the bench tests of a certain prototype. The hyperbolic-tangent functions with different smoothing factors were applied to the profile fitting of step function and piecewise linear function. Then,a discontinuous and non-differential numerical model for the two-staged and three-staged stiffness clutch dampers with asymmetric characteristics,taking into account the hysteresis characteristics,was derived. The numerical model was further modified by using the hyperbolic-tangent function and extended to multi-staged stiffness clutch dampers. Finally,the modified model for the multi-staged stiffness clutch dampers fitting was validated by bench tests of the prototype.