This article discusses the use of deep learning schemes for spoofing detection. Particularly, the characteristics of the so-called Cross Ambiguity Function (CAF) in the presence and absence of spoofing signals are exploited to train a set of data-driven models providing a probabilistic classification. The method operates on a per-satellite basis. The results show that complex neural networks are effectively able to capture the nature of spoofing attacks. Particularly, a Multi-Layer Perceptron (MLP) and two classes of Convolution Neural Networks (CNNs) are considered in this work, validated over simulated data.