A new class of time series models, referred to in this paper as the "periodic transfer function-noise (PTFN) model," has been developed through an extension of conventional nonperiodic (or constant parameter) transfer function-noise (TFN) models. The proposed PTFN model is very flexible, as its form or order and parameter values of both the dynamic and noise components may vary depending on the season of the year. It is shown that Box et al. 's modeling techniques for TFN models can be applied to PTFN models as well. The model has been applied for monthly forecasting of the Ganges River flow using monthly rainfall data of northern India as the predictor. The results are encouraging and suggest that the PTFN class of models has the potential to be useful in capturing the seasonally varying dynamic relationship between a dependent time series and one or more independent time series where each series is interyear stationary but within-year nonstationary.