We present an approach for compensating input delay of arbitrary length in nonlinear control systems. This approach, which due to the infinite dimensionality of the actuator dynamics and due to the nonlinear character of the plant results in a nonlinear feedback operator, is essentially a nonlinear version of the Smith Predictor and its various predictor-based modifications for linear plants. Global stabilization in the presence of arbitrarily long delay is achieved for all nonlinear plants that are globally stabilizable in the absence of delay and that satisfy the property of forward completeness (which is satisfied by most mechanical systems, electromechanical systems, vehicles, and other physical systems). For strict-feedforward systems, one obtains the predictor-based feedback law explicitly. For the linearizable subclass of strict-feedforward systems, closed-loop solutions are also obtained explicitly. The feedback designs are illustrated through two detailed examples.