This paper presents state estimators for previously trained RBF networks based on a minimax approach. The uncertainty class is characterized in terms of an approximation error vector. Minimizing the objective function over this uncertainty class is used to obtain state estimates. The initial portion of the paper presents the derivation and properties of such a minimax state estimator for RBF networks. In the later portion, this is extended to the problem of minimax adaptive state estimation. This approach is useful in the cases where the pretrained RBF network is to be used in state estimation, since the latest information is used in improving estimates of the RBF weights. A special class of estimators for the appended state estimation problem is also considered where a constant gain estimator matrix can be obtained. This section gives sufficient conditions for the existence of such an observer and follows directly from the structure of the RBF networks. Finally, example applications of the minimax and adaptive minimax estimation for nonlinear problems are presented. The results show the accuracy of state estimation using the proposed minimax estimator.