This paper addresses automatic classification of baboon vocalizations. We considered six classes of sounds emitted by "Papio papio" baboons, and report the results of supervised classification carried out with different signal representations (audio features), classifiers, combinations and settings. Results show that up to 94.1\% of correct recognition of pre-segmented elementary segments of vocalizations can be obtained using Mel-Frequency Cepstral Coefficients representation and Support Vector Machines classifiers. Results for other configurations are also presented and discussed, and a possible extension to the "Sound-spotting'' problem, i.e. online joint detection and classification of a vocalization from a continuous audio stream is illustrated and discussed.