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A class of constrained nonlinear 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 asymptotic stabilization, asymptotically tracking reference outputs, etc. Our results for the control of constrained nonlinear systems extend previous results, which are based on linear approximation and linear feedback.