The dynamics of the streamflow in rivers involve nonlinear and multiscale phenomena. An attempt is made to develop nonlinear models combining wavelet decomposition with Volterra models. This paper describes a methodology to develop one-month-ahead forecasts of streamflow using multiscale nonlinear models. The method uses the concept of multiresolution decomposition using wavelets in order to represent the underlying integrated streamflow dynamics and this information, across scales, is then linked together using the first- and second-order Volterra kernels. The model is applied to 30 river data series from the western USA. The mean monthly data series of 30 rivers are grouped under the categories low, medium and high. The study indicated the presence of multiscale phenomena and discernable nonlinear characteristics in the streamflow data. Detailed analyses and results are presented only for three stations, selected to represent the low-flow, medium-flow and high-flow categories, respectively. The proposed model performance is good for all the flow regimes when compared with both the ARMA-type models as well as nonlinear models based on chaos theory.