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A co-actor's intentionality has been suggested to be a key modulating factor for joint action effects like the joint Simon effect (JSE). However, in previous studies intentionality has often been confounded with agency defined as perceiving the initiator of an action as being the causal source of the action. The aim of the present study was to disentangle the role of agency and intentionality as modulating factors of the JSE. In Experiment 1, participants performed a joint go/nogo Simon task next to a co-actor who either intentionally controlled a response button with own finger movements (agency+/intentionality+) or who passively placed the hand on a response button that moved up and down on its own as triggered by computer signals (agency−/intentionality−). In Experiment 2, we included a condition in which participants believed that the co-actor intentionally controlled the response button with a Brain-Computer Interface (BCI) while placing the response finger clearly besides the response button, so that the causal relationship between agent and action effect was perceptually disrupted (agency−/intentionality+). As a control condition, the response button was computer controlled while the co-actor placed the response finger besides the response button (agency−/intentionality−). Experiment 1 showed that the JSE is present with an intentional co-actor and causality between co-actor and action effect, but absent with an unintentional co-actor and a lack of causality between co-actor and action effect. Experiment 2 showed that the JSE is absent with an intentional co-actor, but no causality between co-actor and action effect. Our findings indicate an important role of the co-actor's agency for the JSE. They also suggest that the attribution of agency has a strong perceptual basis.