This paper is concerned with obtaining necessary and sufficient conditions for fulfilling specified state and control pointwise-in-time constraints against a certain class of nonlinear dynamics. The results are generalizations of the maximal output admissible set theory to the case of nonlinear systems. Main contribution of the present paper is to propose explicit algorithmic procedures to determine the maximal output admissible set. Another contribution is that we discuss on a finite determinability of the maximal output admissible set for nonlinear systems. Some relations between observability of nonlinear systems and finite characterizations of the maximal output admissible set are clarified. (C) 2007 Elsevier Ltd. All rights reserved.