Output regulation for a nonlinear plant driven by an exogenous signal is addressed in this paper. In the absence of the standard exosystem hypothesis, we assume availability of the instantaneous values of the exogenous signal and its first time-derivative for use in the control law. We formulate an approximate output regulation problem and characterize solvability in terms of the existence of a certain invariant manifold. The control law we obtain yields a closed-loop system with output exhibiting ultimate boundedness properties with respect to both the first- and the second-time derivatives of the exogenous signal. Performance characteristics are illustrated by application to the linear case and to specific nonlinear examples.