For bilinguals, speaking and listening are assisted by complex control processes including conflict monitoring and inhibition. However, the extent to which these processes adapt to linguistic and situational needs has been examined separately for language production and comprehension. In the present study, we use a dual-EEG to record the carry-over effects of language control on general cognitive control in three language contexts (single-first language [L1], single-second language [L2], and mixed). Chinese learners of English were placed in dyads in which one participant was asked to name pictures while the other listened. Interleaved after each naming/listening trial were flanker trials. The results from picture naming and listening revealed higher delta and theta synchronization in the single-L2 and mixed contexts compared with the single-L1 context and higher theta synchronization in the mixed context compared with the single-L2 and single-L1 contexts. The results from the interleaved flanker trials demonstrated that inhibition was adaptively generalized in the single-L2 and mixed contexts. Altogether, the findings support the natural adaptation of language control to cognitive control and underscore the importance of linguistic context. We argue that these adaptive patterns have the potential to affect corresponding control processes across language and cognitive control tasks.