This paper address the issue of nonlinear model estimation for neural systems with arbitrary point-process inputs using a novel network that is composed of a pre-processing stage of a Laguerre filter bank followed by a single hidden layer with polynomial activation functions. The nonlinear modeling problem for neural systems has been attempted thus far only with Poisson point-process inputs and using cross-correlation methods to estimate low-order nonlinearities. The specific contribution of this paper is the use of the described novel network to achieve practical estimation of the requisite nonlinear model in the case of arbitrary (i.e. non-Poisson) point-process inputs and high-order nonlinearities. The success of this approach has critical implications for the study of neuronal ensembles, for which nonlinear modeling has been hindered by the requirement of Poisson process inputs and by the presence of high-order nonlinearities. The proposed methodology yields accurate models even for short input-output data records and in the presence of considerable noise. The efficacy of this approach is demonstrated with computer-simulated examples having continuous output and point-process output, and with real data from the dentate gyrus of the hippocampus.