Artificial neural networks (ANNs) can be useful in the prediction of hydrologic variables, such as streamflow, particularly when the underlying processes have complex nonlinear interrelationships. However, conventional ANN structures suffer from network training issues that significantly limit their widespread application. This paper presents a multivariate ANN procedure entitled self-organizing linear output map (SOLO), whose structure has been designed for rapid, precise, and inexpensive estimation of network structure/parameters and system outputs. More important, SOLO provides features that facilitate insight into the underlying processes, thereby extending its usefulness beyond forecast applications as a tool for scientific investigations. These characteristics are demonstrated using a classic rainfall-runoff forecasting problem. Various aspects of model performance are evaluated in comparison with other commonly used modeling approaches, including multilayer feedforward ANNs, linear time series modeling, and conceptual rainfall-runoff modeling.