Recent research suggests that we can simultaneously represent the actions of multiple agents in our motor system. However, it is currently unclear exactly how we represent their actions. Here, we tested two competing hypotheses. According to the independence hypothesis, we represent concurrently observed actions as independent, competing actions. According to the compound hypothesis, we instead integrate those actions, whenever possible, into compound actions. In Experiment 1 (N = 32), we first show that the standard imitation-inhibition task with a single hand can be extended to measure automatic imitation of compound actions. In Experiment 2 (N = 55), we then tested how we represent concurrently observed actions by further extending this task to include two hands performing identical or different actions. The results revealed that two hands performing two different actions (e.g., one hand lifts index finger, one hand lifts middle finger) produced an effect similar to that of both hands performing just one of those actions (e.g., both hands lift index finger) but different from that of both hands performing both actions together (e.g., lift both index and middle finger). As such, our results show that concurrently observed actions are coded separately in the motor system.