A notion of kth-order robust control for the nonlinear servomechanism problem is introduced. A transmission zeros condition is given for the existence of a kth-order robust control law such that, regardless of small parameter perturbations of the plant and control law, the closed-loop system will induce a stable invariant manifold with the error map zero up to kth-order at each point of the manifold. Such a control law incorporates an internal model of up to k subsystems determined by the exosystem. A special case of the result of this note recovers the well-known linear robust servomechanism result.