This paper presents a comparative study between different nonlinear damper models, developed for a semi-active Electro-Rheological damper. The first model is developed by extending the hysteresis model to obtain the dynamic characteristic of the damper. To improve the accuracy of capturing the damper's behavior, a nonlinear Bouc-Wen model is developed by using parameter-varying functions of control input and damper state. One of the key points in the proposed models is to describe the dynamics of the controlled portion of the damper force as a first-order system. Hence, the proposed models are adequate for the design and synthesis of Linear Parameter Varying observers and controllers. The model parameters are identified using a simple nonlinear identification procedure. The experimental validation tests are performed on a real 1/5-scaled vehicle testbed of GIPSA-lab, namely INOVE (see www.gipsalab.fr/projet/inove). The results assess the ability and the accuracy of the proposed models to characterize the behaviors of ER dampers.