Linear statistical models ranging in complexity from multivariate regression to canonical correlation analysis (CCA) are commonly used to investigate relationships between two sets of variables. Recently, nonlinear versions of these methods have been implemented via neural network models. Principal predictor analysis (PPA) is a linear technique which fits somewhere between regression and CCA in terms of its architecture. Here a new neural network approach is introduced for performing nonlinear principal predictor analysis (NLPPA). The utility of NLPPA is demonstrated via two test problems. The first, using synthetic data, compares the ability of linear/nonlinear PPA and linear/nonlinear CCA to extract and predict known modes of variability from datasets with increasing noise levels. The NLPPA appears to perform better than the nonlinear CCA under very noisy conditions. The second test, based on real-world data, compares the ability of nonlinear projection (i.e. regression) and NLPPA to explain the response of the Northern Hemisphere winter atmosphere to variations in the sea-surface temperatures in the equatorial Pacific.