In this paper, we report experiments in which we aim to automatically classify primate vocalizations according to four primate species of interest, plus a background category with forest sound events. We compare several standard deep neural networks architectures: standard deep convolutional neural networks (CNNs), MobileNets and ResNets. To tackle the small size of the training dataset, less than seven thousand audio files, the data augmentation techniques SpecAugment and MixUp proved to be very useful. Against the very unbalanced classes of the dataset, we used a balanced data sampler that showed to be efficient. An exponential moving average of the model weights allowed to get slight further gains. The best model was a standard 10-layer CNN, comprised of about five million parameters. It achieved a 93.6% Unweighted Average Recall (UAR) on the development set, and generalized well on the test set with a 92.5% UAR, outperforming an official baseline of 86.6%. We quantify the performance gains brought by the augmentations and training tricks, and report fusion and classification experiments based on embeddings that did not bring better results.