Performing several actions simultaneously usually yields interference, which is commonly explained by referring to theoretical concepts such as crosstalk and structural limitations associated with response selection. While most research focuses on dual-task scenarios (involving two independent tasks), we here study the role of response selection and crosstalk for the control of cross-modal response compounds (saccades and manual responses) triggered by a single stimulus. In two experiments, participants performed single responses and spatially compatible versus incompatible dual-response compounds (crosstalk manipulation) in conditions with or without response selection requirements (i.e., responses either changed randomly between trials or were constantly repeated within a block). The results showed that substantial crosstalk effects were only present when response (compound) selection was required, not when a pre-selected response compound was merely repeated throughout a block of trials. We suggest that cross-response crosstalk operates on the level of response selection (during the activation of response codes), not on the level of response execution (when participants can rely on pre-activated response codes). Furthermore, we observed substantial residual dual-response costs even when neither response incompatibility nor response selection requirements were present. This suggests additional general dual-execution interference that occurs on a late, execution-related processing stage and even for two responses in rather distinct (manual and oculomotor) output modules. Generally, the results emphasize the importance of considering oculomotor interference in theorizing on multiple-action control.