The problem of finding an input-output representation of a nonlinear state space system, usually referred to as the state elimination, plays an important role in certain control problems. Though, it has been shown that such a representation, at least locally, always exists for both the systems with and without delays, it might be a neutral input-output differential equation in the former case, even when one starts with a retarded system. In this paper the state elimination is therefore extended further to nonlinear neutral state-space systems, and it is shown that also in such a case an input-output representation, at least locally, always exists. In general, it represents a neutral system again. Computational aspects related to the state elimination problem are discussed as well.