In this study, the forecasting capabilities of a new class of nonlinear econometric models, namely, the LSTAR-LST-GARCH-RBF and MLP models are evaluated. The models are utilized to model and to forecast the daily returns of crude oil prices. Many financial time series are subjected to leptokurtic distribution, heavy tails, and nonlinear conditional volatility. This characteristic feature leads to deterioration in the forecast capabilities of traditional models such as the ARCH and GARCH models.According to the empirical findings, the oil prices and their daily returns could be classified as possessing nonlinearity in the conditional mean and conditional variance processes.Several model groups are evaluated:(i) the models proposed in the first group are the LSTAR-LST-GARCH models that are augmented with fractional integration and asymmetric power terms(FIGARCH, APGARCH, and FIAPGARCH);(ii) the models proposed in the second group are the LSTAR-LST-GARCH models further augmented with MLP and RBF type neural networks. The models are compared in terms of MSE, RMSE, and MAE criteria for in-sample and out-of-sample forecast capabilities. The results show that the LSTAR based and neural network augmented models provide important gains over the single-regime baseline GARCH models, followed by the LSTAR-LST-GARCH type models in terms of modeling and forecasting volatility in crude oil prices. The models are utilized to model and to forecast the daily returns of crude oil prices. Many financial time series are subjected to leptokurtic distribution, heavy tails, and nonlinear conditional volatility. This characteristic feature leads to deterioration in the forecast capabilities of traditional models such as the ARCH and GARCH models. According to the empirical findings, the oil prices and their daily returns could be classified as possessing nonlinearity in the conditional mean and conditional variance processes. (2) the models proposed in the first group are the LSTAR-LST-GARCH models that are augmented with fractional integration and asymmetric power terms (FIGARCH, APGARCH, and FIAPGARCH); (ii) the models proposed in the second group are the LSTAR-LST-GARCH models further augmented with MLP and RBF type neural networks. The models are compared in terms of MSE, RMSE, and MAE criteria for in-sample and out-of-sample forecast capabilities. The results show that the LSTAR based and neural network augmented models provide important gains over the the single-regime baseline GARCH models, followed by the LSTAR-LST-GARCH type models in terms of modeling and forecasting volatility in crude oil prices.