The two-process model of sleep regulation has been applied successfully to describe, predict, and understand sleep–wake regulation in a variety of experimental protocols such as sleep deprivation and forced desynchrony. A non-linear interaction between the homeostatic and circadian processes was reported when the model was applied to describe alertness and performance data obtained during forced desynchrony. This non-linear interaction could also be due to intrinsic non-linearity in the metrics used to measure alertness and performance, however. Distinguishing these possibilities would be of theoretical interest, but could also have important implications for the design and interpretation of experiments placing sleep at different circadian phases or varying the duration of sleep and/or wakefulness. Although to date no resolution to this controversy has been found, here we show that the issue can be addressed with existing data sets. The interaction between the homeostatic and circadian processes of sleep–wake regulation was investigated using neurobehavioural performance data from a laboratory experiment involving total sleep deprivation. The results provided evidence of an actual non-linear interaction between the homeostatic and circadian processes of sleep–wake regulation for the prediction of waking neurobehavioural performance.