A crucial demand in dual tasks suffering from a capacity limited processing mechanism is task-order scheduling, i.e. the control of the order in which the two component tasks are processed by this limited processing mechanism. The present study aims to test whether the lateral prefrontal cortex (LPFC) is associated with this demand. For this, 15 participants performed a psychological refractory paradigm (PRP) type dual task in an event-related functional magnetic resonance (fMRI) experiment. In detail, two choice reaction tasks, a visual (response with right hand) and an auditory (response with left hand), were presented with a temporal offset of 200 ms, while the participants were required to respond to the tasks in the order of their presentation. Importantly, the presentation order of the tasks changed randomly. Based on previous evidence, we argue that trials in which the present task order changed as compared to the previous trial (different-order trials) impose higher demands on task coordination than same-order trials do. The analyses showed that cortical areas along the posterior part of the left inferior frontal sulcus as well as the right posterior middle frontal gyrus were more strongly activated in different-order than in same-order trials, thus supporting the conclusion that one function of the LPFC for dual-task performance is the temporal coordination of two tasks. Furthermore, it is discussed that the present findings favour the active scheduling over the passive queuing hypothesis of dual-task processing.