In stream flow series modeling by the conventional time series models (AutoRegressive Moving Average - ARMA) under the assumption of constant variance, the mean behavior of the process is focused on and the non-linear effects based on variance behavior are neglected. Modeling of this nonlinear phenomenon with variance behavior and water resource management of hydrological processes which involve risk and uncertainty gains importance. This is true for modeling with Auto Regressive Conditional Heteroskedasticity (ARCH) or with its general form, Generalized Auto Regressive Conditional Heteroskedasticity (GARCH). In this study, the mean behavior of the daily and yearly stream flow series of the Koprucay River is modeled with the linear time series models (AR, MA, ARMA) and the best fit models are selected. The volatility presence is searched by using the Engle's Lagrange Multiplier (LM) Test on the residuals from the linear models, and the conditional heteroskedastic variance models (ARCH-GARCH) are developed. It is shown that the ARCH effect in the daily stream flow series can best be modeled with ARMA(1,1)-GARCH(2,3) and the volatility does not exist in the yearly stream flow series. The volatility clustering in daily stream flow series is shown with the conditional standard deviation and variance graphs. It is expected that, this study can be a useful contribution to the statistical modeling of stream flow processes.