--- - |2+ Key points In most patients with obstructive sleep apnoea (OSA), there is a spontaneous resolution of the breathing disorders during slow wave sleep (SWS) for yet unknown reasons related to non‐anatomical factors. Some recently identified forms of neural memory specific of upper airway muscles may play a role in this phenomenon. In the present study, we show for the first time that a form of memory of the genioglossus (tongue) muscle is greatly enhanced during SWS compared to non‐rapid eye movement stage 2 sleep. The present study represents a step forward in understanding the mechanisms responsible for the spontaneous development of stable breathing during SWS in OSA patients and may help the discovery of novel therapeutic strategies for this disease. Abstract Several studies have shown that obstructive sleep apnoea (OSA) improves during slow wave sleep (SWS) for reasons that remain unclear. Recent studies have identified forms of neural memory such as short‐term potentiation or after‐discharge that can occur in response to upper airway obstruction. Neural memory may play a role in the development of stable breathing during SWS by increasing upper airway muscles activity in this sleep stage. We hypothesize that the after‐discharge of the genioglossus muscle following upper airway obstruction is enhanced during SWS compared to non‐rapid eye movement stage 2 (N2). During sleep, we performed five‐breath drops in continuous positive airway pressure (CPAP‐drop) to simulate obstructive events and reflexively activate the genioglossus. Immediately afterwards, CPAP was returned to an optimal level. Once the post‐drop ventilation returned to eupnoea, the genioglossus after‐discharge was measured as the time it took for genioglossus activity to return to baseline levels. In total, 171 CPAP‐drops were analysed from a group of 16 healthy subjects and 19 OSA patients. A mixed‐model analysis showed that after‐discharge duration during SWS was 208% (95% confidence interval = 112% to 387%, P = 0.022) greater than during N2 after adjusting for covariates (ventilatory drive, CPAP levels). There was also a non‐significant trend for a –35% reduction in after‐discharge duration following an arousal vs. no‐arousal from sleep (95% confidence interval = –59.5% to 5%, P = 0.08). Genioglossus after‐discharge is two‐fold greater in SWS vs. N2, which could partly explain the breathing stabilization described in OSA patients during this sleep stage. - 'The Journal of Physiology, Volume 596, Issue 21, Page 5163-5173, 1 November 2018. '