Cognitive demand is thought to modulate two often used, but rarely combined, measures: pupil size and neural alpha (8-12 Hz) oscillatory power. However, it is unclear whether these two measures capture cognitive demand in a similar way, and whether a measured cognitive demand response in pupil size or brain activity is dependent on sensory modality by which the demand is induced. Here we recorded pupil size and neural alpha power (using electroencephalography), while human participants of both sexes concurrently performed a visual multiple object-tracking task and an auditory gap-detection task. Difficulties of the two tasks were manipulated independent of each other. Participants' performance decreased in accuracy and speed with increasing cognitive demand. Pupil size increased with increasing demand for both the auditory and the visual task. Alpha power emerging from two cortical sources showed counteracting neural dynamics: Alpha power in visual cortex decreased with increasing demand in the visual task, whereas alpha power in parietal cortex increased with increasing demand in the auditory task. Furthermore, demand-related changes in pupil size and alpha power were uncorrelated, suggesting that they index different aspects of cognitive demand. Overall, the current study demonstrates that the dynamics of the neurophysiological indices of cognitive demand and associated effort are multi-faceted and potentially modality-dependent under complex audio-visual task conditions.