Polycyclic aromatic hydrocarbons (PAHs) are ubiquitous pollutants of high environmental concern. The experimental data of a mutagenicity test on human B-lymphoblastoid cells (alternative to the Ames bacterial test) for a set of 70 oxo-, nitro- and unsubstituted PAHs, detected in particulate matter (PM), were modelled by Quantitative Structure-Activity Relationships (QSAR) classification methods (k-NN, k-Nearest Neighbour, and CART, Classification and Regression Tree) based on different theoretical molecular descriptors selected by Genetic Algorithms. The best models were validated for predictivity both externally and internally. For external validation, Self Organizing Maps (SOM) were applied to split the original data set. The best models, developed on the training set alone, show good predictive performance also on the prediction set chemicals (sensitivity 69.2-87.1%, specificity 62.5-87.5%). The classification of PAHs according to their mutagenicity, based only on a few theoretical molecular descriptors, allows a preliminary assessment of the human health risk, and the prioritisation of these compounds.