The study focuses on a new class of nonlinear volatility models based on neural networks and STAR type nonlinearity. Accordingly, LSTAR-LST-GARCH family and LSTAR-LST-GARCH-NN family of models will be evaluated to analyze petrol prices with economic applications. The nonlinear behavior and leptokurtic distribution are discussed in many studies. The study aims proposing augmentation of linear GARCH, fractionally integrated FI-GARCH and Asymmetric Power APGARCH models with LSTAR type nonlinearity modeling. Further, the proposed models will be augmented with neural networks to benefit from well known learning and forecasting capabilities. The multilayer perceptron (MLP) neural network model and LSTAR model have significant similarities in terms of their architecture. The proposed LSTAR-LST-GARCH family and ANN augmented LSTAR-LST-GARCH-MLP models are evaluated for modeling petrol prices. Empirical findings of the study are: (1) Fractionally integrated and asymmetric power improvements among the GARCH family models provide better forecasting capability for petrol prices; better captured long memory and high volatility characteristics of petrol prices. (2). LSTAR-LST-GARCH model family results in even better gains in out-of-sample forecasting. (3) Donaldson and Kamstra (1997) based MLP-GARCH family provided similar results with the LSTAR-LST-GARCH family models. One exception is for MLP-FIGARCH and MLP-FIAPGARCH models; FI and AP augmented models proposed in this study. (4) Volatility clustering, asymmetry and nonlinearity characteristics of petrol prices are best captured with the LSTAR-LST-GARCH-MLP model family. Forecasting capabilities of neural network techniques are promising. Among the evaluated models, the LSTAR-LST-APGARCH-MLP model provided the best performance overall. With a political perspective, in addition to the highly volatile structure, the long memory characteristics of petrol prices requires that the economic policy interventions should be kept at the modest levels to avoid persistent impacts of shocks. (C) 2013 Elsevier B.V. All rights reserved.