The steady-state and transient accuracy of magnetorheological fluid (MRF) clutch torque control is affected by the magnetic hysteresis and eddy current lag. The paper presents a nonlinear analytical model of the MRF clutch electromagnetic circuit dynamics. The model includes two state variables describing the combined solenoid and eddy current dynamics, and the dynamics induced by the magnetic hysteresis effect. The overall nonlinear model is experimentally validated under the clutch current-control conditions. It is demonstrated that the use of second state variable for magnetic hysteresis significantly improves the modeling accuracy when compared to the more traditional first-order linear model.