Both the putative mirror neuron system (pMNS) and the ventral medial prefrontal cortex (vmPFC) are deemed important for social interaction: the pMNS because it supposedly "resonates" with the actions of others, the vmPFC because it is involved in mentalizing. Strictly speaking, the resonance property of the pMNS has never been investigated. Classical functional MRI experiments have only investigated whether pMNS regions augment their activity when an action is seen or executed. Resonance, however, entails more than only "going on and off together". Activity in the pMNS of an observer should continuously follow the more subtle changes over time in activity of the pMNS of the actor. Here we directly explore whether such resonance indeed occurs during continuous streams of actions. We let participants play the game of charades while we measured brain activity of both gesturer and guesser. We then applied a method to localize directed influences between the brains of the participants: between-brain Granger-causality mapping. Results show that a guesser's brain activity in regions involved in mentalizing and mirroring echoes the temporal structure of a gesturer's brain activity. This provides evidence for resonance theories and indicates a fine-grained temporal interplay between regions involved in motor planning and regions involved in thinking about the mental states of others. Furthermore, this method enables experiments to be more ecologically valid by providing the opportunity to leave social interaction unconstrained. This, in turn, would allow us to tap into the neural substrates of social deficits such as autism spectrum disorder.