The regulation of the timing of sleep is thought to be linked to the temporal dynamics of slow-wave activity [SWA, electroencephalogram (EEG) spectral power in the ∼0.75–4.5 Hz range] in the cortical non-rapid eye movement (NREM) sleep EEG. In the two-process model of sleep regulation, SWA was used as a direct indication of sleep debt, or Process S. Originally, estimation of the latter was performed in a gross way, by measuring average SWA across NREM–REM sleep cycles, fitting an exponential curve to the values thus obtained and estimating its time constant. In later studies, SWA was assumed to be proportional to the instantaneous decay rate of Process S, rather than taken as a direct reflection of S. Following up on this, we extended the existing model of SWA dynamics in which the effects of intrusions of REM sleep and wakefulness were incorporated. For each subject, a ‘gain constant’ can be estimated that quantifies the efficiency of SWA in dissipating S. As the course of SWA is variable across cortical locations, local differences are likely to exist in the rate of discharge of S, eventually leading to different levels of S in different cortical regions. In this study, we estimate the extent of local differences of SWA regulation on the basis of the extended model of SWA dynamics, for 26 locations on the scalp. We observed higher efficiency of SWA in dissipation of S in frontal EEG derivations, suggesting that SWA regulation has a clear local aspect. This result further suggests that the process involved in (local) SWA regulation cannot be identical to the Process S involved (with Process C) in effectual determination of sleep timing – a single behaviour that cannot vary between locations on the scalp. We therefore propose to distinguish these two representations and characterize the former, purely SWA-related, as ‘Process Z’, which then is different for different locations on the scalp. To demonstrate those differences, we compare the gain constants derived for the medial EEG derivations (Fz, Cz, Pz, Oz) with each other and with the decay rate derived from SWA values per NREM–REM sleep cycle.