One of the most important problems in hydrology is the reliable forecasting of maximum discharge at an ungauged site of interest. Statistical techniques are commonly used for finding the maximum discharge and return period relationship. However, these techniques are generally considered to be inadequate because of the complexity of the problem. Hence, neural network techniques are preferred. In this study, two different neural network models developed based on the following techniques - a multi-layer perceptron neural network with Levenberg-Marquardt algorithm and a radial basis neural network behind an adaptive neuro-fuzzy inference system - are employed in order to capture the nonlinear relationship between discharge and five independent variables - drainage area (km(2)), elevation (m), latitude, longitude, return period (year) and maximum discharge (m(3)/s). For a modeling study, watershed data from 543 catchments across Turkey were used. Statistical models with regression techniques were also applied to the same data, providing a wider comparison. The results of the models were then compared and assessed with respect to mean square errors, mean absolute error, mean absolute relative error and determination coefficient. Based on these results, it was found that the neural network techniques demonstrated better performance in predicting the maximum discharge based on five independent variables than the regression techniques, and were comparable to the adaptive neuro-fuzzy inference system.