A class of nonlinear constrained dynamic systems is studied. We first characterize the constrained submanifold and the constrained dynamics without using the vector relative degree. Applying the nonlinear feedback and exact linearization techniques to constrained systems, we discuss several control problems for the constrained dynamics such as asymptotically stabilization, asymptotically tracking reference outputs. Our results for the control of constrained nonlinear systems extend previous results, which is based on linear approximation and linear feedback.