New psychoactive drugs that are leading to severe intoxications are constantly seized on the European black market. Recent studies indicate that most of these new substances are synthetic cannabinoids and hallucinogenic amphetamines. In this study, we are presenting the results obtained with an expert system that was built to identify automatically the class identity of these types of drugs of abuse, based on their Attenuated Total Reflection-Fourier Transform Infrared (ATR-FTIR) spectra processed with Convolutional Neural Networks (CNNs). CNNs have been applied with great success in recent years in various computer applications, such as image classification, but little work has been done in using this kind of deep learning models for spectral data classification. The aim of this study was to improve the detection accuracy (classification performance) that we have already obtained with other statistical mathematics and artificial intelligence techniques. The performances of the CNN system are discussed in comparison with those of the later models.