Joint attention consists in following another's gaze onto an environmental object, which leads to the alignment of both subjects' attention onto this object. It is a fundamental mechanism of non-verbal communication, and it is essential for dynamic, online, interindividual synchronization during interactions. Here we aimed at investigating the oscillatory brain correlates of joint attention in a face-to-face paradigm where dyads of participants dynamically oriented their attention toward the same or different objects during joint and no-joint attention periods respectively. We also manipulated task instruction: in socially driven instructions, the participants had to follow explicitly their partner's gaze, while in color-driven instructions, the objects to be looked at were designated at by their color so that no explicit gaze following was required. We focused on oscillatory activities in the 10 Hz frequency range, where parieto-occipital alpha and the centro-parietal mu rhythms have been described, as these rhythms have been associated with attention and social coordination processes respectively. We tested the hypothesis of a modulation of these oscillatory activities by joint attention. We used dual-EEG to record simultaneously the brain activities of the participant dyads during our live, face-to-face joint attention paradigm. We showed that joint attention periods - as compared to the no-joint attention periods - were associated with a decrease of signal power between 11 and 13 Hz over a large set of left centro-parieto-occipital electrodes, encompassing the scalp regions where alpha and mu rhythms have been described. This 11-13 Hz signal power decrease was observed independently of the task instruction: it was similar when joint versus no-joint attention situations were socially driven and when they were color-driven. These results are interpreted in terms of the processes of attention mirroring, social coordination, and mutual attentiveness associated with joint attention state.