Doing two things at once is difficult. When two tasks have to be performed within a short interval, the second is sharply delayed, an effect called the Psychological Refractory Period (PRP). Similarly, when two successive visual targets are briefly flashed, people may fail to detect the second target (Attentional Blink or AB). Although AB and PRP are typically studied in very different paradigms, a recent detailed neuromimetic model suggests that both might arise from the same serial stage during which stimuli gain access to consciousness and, as a result, can be arbitrarily routed to any other appropriate processor. Here, in agreement with this model, we demonstrate that AB and PRP can be obtained on alternate trials of the same cross-modal paradigm and result from limitations in the same brain mechanisms. We asked participants to respond as fast as possible to an auditory target T1 and then to a visual target T2 embedded in a series of distractors, while brain activity was recorded with magneto-encephalography (MEG). For identical stimuli, we observed a mixture of blinked trials, where T2 was entirely missed, and PRP trials, where T2 processing was delayed. MEG recordings showed that PRP and blinked trials underwent identical sensory processing in visual occipito-temporal cortices, even including the non-conscious separation of targets from distractors. However, late activations in frontal cortex (> 350 ms), strongly influenced by the speed of task-1 execution, were delayed in PRP trials and absent in blinked trials. Our findings suggest that PRP and AB arise from similar cortical stages, can occur with the same exact stimuli, and are merely distinguished by trial-by-trial fluctuations in task processing.