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This paper presents a neural network-based anomaly detection system for vehicular communications. The proposed system is able to detect in-vehicle data tampering in order to avoid the transmission of bogus or harmful information. We investigate the use of Long Short-term Memory (LSTM) and Multilayer Perceptron (MLP) neural networks to build two prediction models. For each model, an efficient architecture is designed based on appropriate hardware requirements. Then, a comparative performance analysis is provided to recommend the most efficient neural network model. Finally, a set of metrics are selected to show the accuracy of the proposed detection system under several types of security attacks.