Single- and multiple-input transfer function (TF) models and their applications in modeling streamflow systems are reviewed. To account for nonlinearities in streamflows, a procedure for generating the two most important inputs, snowmelt and effective rain, using nonlinear filters is proposed. A multiple-input TF model identification procedure that uses a vector autoregressive model and the Corner method is proposed. These procedures are illustrated using 3 years of daily data for the Saugeen River near Port Elgin in Ontario, Canada. The final TF model was found to be very parsimonious and more accurate (in terms of mean-squared error) than the more complex, nonlinear Nested Threshold AutoRegressive model. ¿ 1998 American Geophysical Union