Significance The brain’s remarkable capacity for language requires bidirectional interactions between functionally specialized brain regions. Although the functional role of individual regions in the brain network for language has been well studied, as of yet little is known about the mechanisms that facilitate the information exchange between these brain regions. In this paper we show that communication between language-relevant areas in the brain is supported by rhythmic neuronal synchronization and that different rhythms reflect the direction of information flow. These findings likely reflect a generic mechanism that allows for dynamic routing of information in a network of task-relevant brain regions during cognitive processing.