The psychological refractory period (PRP) refers to the fact that humans typically cannot perform two tasks at once. Behavioral experiments have led to the proposal that, in fact, peripheral perceptual and motor stages continue to operate in parallel, and that only a central decision stage imposes a serial bottleneck. We tested this model using neuroimaging methods combined with innovative time-sensitive analysis tools. Subjects performed a dual-task visual-auditory paradigm in which a delay of 300 ms was injected into the auditory task either within or outside of the dual-task interference period. Event-related potentials indicated that the first approximately 250 ms of processing were insensitive to dual-task interference, and that the PRP was mainly reflected in a delayed global component. By a clustering analysis based on time-resolved functional magnetic resonance imaging, we identified networks with qualitatively different timing properties: sensory areas tracked the objective time of stimulus presentation, a bilateral parietoprefrontal network correlated with the PRP delay, and an extended bilateral network that included bilateral posterior parietal cortex, premotor cortex, supplementary motor area, anterior part of the insula, and cerebellum was shared by both tasks during the extent of dual-task performance. The results provide physiological evidence for the coexistence of serial and parallel processes within a cognitive task.