Dual-task (DT) situations require additional control processes that actively schedule the sequence of task processing. These control processes rely on an order representation, the task-order set, that contains explicit information about the processing order of the component tasks and that is activated during DT processing. Evidence for this assumption stems from the observation that, in DT situations with a random task order, performance is usually improved in trials with a repeated (same-order trial) compared with a reversed (different-order trial) order of tasks relative to the preceding trial. In the current study, we tested whether performing only one of the two component tasks is sufficient to activate the task-order set. For this purpose, participants performed an auditory-visual DT with random task order while in some trials they only performed the first (Experiment 1) or the second (Experiment 2) component task. We found improved DT performance in same-order compared with different-order trials following trials in which only task 1 was performed. This performance benefit for same-order trials, however, was not observable after trials in which only task 2 was performed. This finding suggests that the processing of task 1 but not of task 2 is sufficient for the activation of the task-order set in DT situations.