Recently, Artificial Neural Network (ANN) methods, which have been successfully applied in many fields, have been considered for a large number of reliable streamflow estimation and modeling studies for the design and project planning of hydraulic structures. The present study aimed to model the rainfall–runoff relationship using different ANN methods. The Nergizlik Dam, located in the Seyhan sub-basin and one of the important basins in Turkey, was chosen as the study area. Analyses were carried out based on streamflow estimation with the help of observed precipitation and runoff data at certain time intervals. Feed Forward Backpropagation Neural Network (FFBPNN) and Generalized Regression Neural Network (GRNN) methods were adopted, and obtained results were compared with Multiple Linear Regression (MLR) method, which is accepted as the traditional method. Also, the models were performed using three different transfer functions to create optimum ANN modeling. As a result of the study, it was seen that ANN methods showed statistically good results in rainfall–runoff modeling, and the developed models can be successfully applied in the estimation of average monthly flows.