Recent research suggests that we can simultaneously represent the actions of multiple agents in our motor system. However, it is unclear exactly how concurrently observed actions are represented. Here, we tested two competing hypotheses. According to the independence hypothesis, concurrently observed actions are represented as independent actions. According to the compound hypothesis, they are instead integrated, 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 Experiments 2-5 (NTotal = 368), we then investigated the representation of concurrently observed actions by further extending this task to include two hands. The results showed 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 (i.e., a compound action; lift both index and middle finger). This indicates that concurrently observed actions are coded as independent actions in the motor system. Public Significance Statement This study shows that concurrently observed actions are not integrated into compound actions, suggesting that the actions of different agents are processed independently in the motor system.