We present a global stabilization procedure for nonlinear cascade and feedforward systems which extends the existing stabilization results, Our main tool is the construction of a Lyapunov function for a class of (globally stable) uncontrolled cascade systems, This construction serves as a basis for a recursive controller design for cascade and feedforward systems. We give conditions for continuous differentiability of the Lyapunov function and the resulting control law and propose methods for their exact and approximate computation.