An algorithmic method is proposed to design stabilizing control laws for a class of nonlinear systems that comprises single-input feedback-linearizable systems and a particular set of single-input non feedback-linearizable systems. The method proceeds iteratively and consists of two stages; it converts the system into cascade form and reduces the dimension at every step in the forward stage, while it constructs the feedback law iteratively as well in the backward stage. Controller design proceeds via the design of invariant manifolds and includes a guarantee of stability at every step. The paper shows that the construction of these invariant manifolds is well defined for feedback-linearizable system and, furthermore, it can also be applied to a class of non feedback-linearizable systems. These features are illustrated via two simulation examples.