Many common behaviours require people to coordinate the timing of their actions with the timing of others' actions. We examined whether representations of musicians' actions are activated in coperformers with whom they must coordinate their actions in time and whether coperformers simulate each other's actions using their own motor systems during temporal coordination. Pianists performed right-hand melodies along with simple or complex left-hand accompaniments produced by themselves or by another pianist. Individual performers' preferred performance rates were measured in solo performance of the right-hand melody. The complexity of the left-hand accompaniment influenced the temporal grouping structure of the right-hand melody in the same way when it was performed by the self or by the duet partner, providing some support for the action corepresentation hypothesis. In contrast, accompaniment complexity had little influence on temporal coordination measures (asynchronies and cross-correlations between parts). Temporal coordination measures were influenced by a priori similarities between partners' preferred rates; partners who had similar preferred rates in solo performance were better synchronized and showed mutual adaptation to each other's timing during duet performances. These findings extend previous findings of action corepresentation and action simulation to a task that requires precise temporal coordination of independent yet simultaneous actions.