The topic of this paper is the identification of an accurate model for magneto-rheological (MR) dampers. A semi-active MR-damper is a dynamic system, where the inputs are the elongation velocity and the command current; the current is the control input which modulates at high-bandwidth the damping characteristic through the variation of a magnetic field. The output is the force delivered by the damper. Among the broad set of applications where MR-dampers can be used, the results proposed in this work refer to MR-dampers for the control of vehicle dynamics. MR-damper are highly non-linear systems, and their accurate modeling is a non-trivial task. MR-dampers can be modeled using two different model classes: semi-physical models and black-box models. Both approaches are considered in this work. The purpose of this brief paper is to make a concise but complete presentation and discussion of a non-trivial system identification problem. The problem considered herein is particularly interesting from the system identification point of view: from one side, the MR-damper is a very attractive actuator, which is likely to become the key device for many dynamics and vibration control systems in the near future; on the other side, it is an example of an application problem where the accurate modeling of the actuation device is one of the most crucial part of the whole control design problem. (C) 2004 Elsevier Ltd. All rights reserved.