A key goal in the study of visual processing is to obtain a comprehensive description of the relationship between visual stimuli and neuronal responses. One way to guide the search for models is to use a general nonparametric regression algorithm, such as a neural network. We have developed a multilayer feed-forward network algorithm that can be used to characterize nonlinear stimulus-response mapping functions of neurons in primary visual cortex (area V1) using natural image stimuli. The network is capable of extracting several known V1 response properties such as: orientation and spatial frequency tuning, the spatial phase invariance of complex cells, and direction selectivity. We present details of a method for training networks and visualizing their properties. We also compare how well conventional explicit models and those developed using neural networks can predict novel responses to natural scenes.