A regional flood frequency analysis based on the index flood method is applied using probability distributions commonly utilized for this purpose. The distribution parameters are calculated by the method of L-moments with the data of the annual flood peaks series recorded at gauging sections of 13 unregulated natural streams in the East Mediterranean River Basin in Turkey. The artificial neural networks (ANNs) models of (1) the multi-layer perceptrons (MLP) neural networks, (2) radial basis function based neural networks (RBNN), and (3) generalized regression neural networks (GRNN) are developed as alternatives to the L-moments method. Multiple-linear and multiple-nonlinear regression models (MLR and MNLR) are also used in the study. The L-moments analysis on these 13 annual flood peaks series indicates that the East Mediterranean River Basin is hydrologically homogeneous as a whole. Among the tried distributions which are the Generalized Logistic, Generalized Extreme Vaules, Generalized Normal, Pearson Type III, Wakeby, and Generalized Pareto, the Generalized Logistic and Generalized Extreme Values distributions pass the Z statistic goodness-of-fit test of the L-moments method for the East Mediterranean River Basin, the former performing yet better than the latter. Hence, as the outcome of the L-moments method applied by the Generalized Logistic distribution, two equations are developed to estimate flood peaks of any return periods for any un-gauged site in the study region. The ANNs, MLR and MNLR models are trained and tested using the data of these 13 gauged sites. The results show that the predicting performance of the MLP model is superior to the others. The application of the MLP model is performed by a special Matlab code, which yields logarithm of the flood peak, Ln(Q(T)), versus a desired return period, T.