We assessed the role of alpha-band oscillatory activity during a task-switching design that required participants to switch between an auditory and a visual task, while task-relevant audiovisual inputs were simultaneously presented. Instructional cues informed participants which task to perform on a given trial and we assessed alpha-band power in the short 1.35-s period intervening between the cue and the task-imperative stimuli, on the premise that attentional biasing mechanisms would be deployed to resolve competition between the auditory and visual inputs. Prior work had shown that alpha-band activity was differentially deployed depending on the modality of the cued task. Here, we asked whether this activity would, in turn, be differentially deployed depending on whether participants had just made a switch of task or were being asked to simply repeat the task. It is well established that performance speed and accuracy are poorer on switch than on repeat trials. Here, however, the use of instructional cues completely mitigated these classic switch-costs. Measures of alpha-band synchronisation and desynchronisation showed that there was indeed greater and earlier differential deployment of alpha-band activity on switch vs. repeat trials. Contrary to our hypothesis, this differential effect was entirely due to changes in the amount of desynchronisation observed during switch and repeat trials of the visual task, with more desynchronisation over both posterior and frontal scalp regions during switch-visual trials. These data imply that particularly vigorous, and essentially fully effective, anticipatory biasing mechanisms resolved the competition between competing auditory and visual inputs when a rapid switch of task was required.