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Social interactions are made of complex behavioural actions that might be found in all mammalians, including humans and rodents. Recently, mouse models are increasingly being used in preclinical research to understand the biological basis of social-related pathologies or abnormalities. However, reliable and flexible automatic systems able to precisely quantify social behavioural interactions of multiple mice are still missing. Here, we present a system built on two components. A module able to accurately track the position of multiple interacting mice from videos, regardless of their fur colour or light settings, and a module that automatically characterise social and non-social behaviours. The behavioural analysis is obtained by deriving a new set of specialised spatio-temporal features from the tracker output. These features are further employed by a learning-by-example classifier, which predicts for each frame and for each mouse in the cage one of the behaviours learnt from the examples given by the experimenters. The system is validated on an extensive set of experimental trials involving multiple mice in an open arena. In a first evaluation we compare the classifier output with the independent evaluation of two human graders, obtaining comparable results. Then, we show the applicability of our technique to multiple mice settings, using up to four interacting mice. The system is also compared with a solution recently proposed in the literature that, similarly to us, addresses the problem with a learning-by-examples approach. Finally, we further validated our automatic system to differentiate between C57B/6J (a commonly used reference inbred strain) and BTBR T+tf/J (a mouse model for autism spectrum disorders). Overall, these data demonstrate the validity and effectiveness of this new machine learning system in the detection of social and non-social behaviours in multiple (>2) interacting mice, and its versatility to deal with different experimental settings and scenarios.