The detection of illicit radiological materials is critical to establishing a robust second line of defence in nuclear security. Neutron-capture prompt-gamma activation analysis (PGAA) can be used to detect multiple radioactive materials across the entire Periodic Table. However, long detection times and a high rate of false positives pose a significant hindrance in the deployment of PGAA-based systems to identify the presence of illicit substances in nuclear forensics. In the present work, six different machine-learning algorithms were developed to classify radioactive elements based on the PGAA energy spectra. The model performance was evaluated using standard classification metrics and trend curves with an emphasis on comparing the effectiveness of algorithms that are best suited for classifying imbalanced datasets. We analyse the classification performance based on Precision, Recall, F1-score, Specificity, Confusion matrix, ROC-AUC curves, and Geometric Mean Score (GMS) measures. The tree-based algorithms (Decision Trees, Random Forest and AdaBoost) have consistently outperformed Support Vector Machine and K-Nearest Neighbours. Based on the results presented, AdaBoost is the preferred classifier to analyse data containing PGAA spectral information due to the high recall and minimal false negatives reported in the minority class.