We are currently working on a series of machine learning experiments with the goal of understanding the mechanisms of turn-taking transitions in dialogue. We base our experiments on features automatically extracted from speech and EEG signals. For this purpose, we built a corpus of unrestricted dialogues between pairs of subjects, with simultaneous recordings of speech and EEG from both subjects. The problems we work with deal strongly with signal processing of human speech and brain cortex electrical activity. Our approach is focused on exploiting and creating novel computational techniques in the area of pattern recognition in sequential data. These results may lead to new tools valuable for the development of brain-computer interfaces.