An investigation is made to the friction chutch engagement control of automotive AMT systems based on a nonlinear dynamic model with double inputs. According to friction torque transmission characteristics during clutch engagement, an equivalent, fully controllable and linearized model and the feedback linearization control are derived from the original system with nonlinearities via homomorphic transforms. By the resulting mathematical modeling, computer simulations are made both for the original nonlinear and feedback linearized systems with incorporation of ordinary PID controllers to follow ideal vehicle dynamic responses. It has been shown by comparison between the two sets of numerical results that the feedback linearization control designed for the nonlinear system is of fine accuracy and robustness in model tracking behaviors of clutch engagements.