Obstructive sleep apnea (OSA) patients are exposed to nighttime hypoxia during sleep by intermittent airway closure and feel daytime strong sleepiness. Strangely, insomnia co-occur in some OSA patients, which is called co-morbid insomnia and sleep apnea (COMISA). Here, we show activity responses to daytime hypoxia (DHx) in nocturnal mice were comparable to daytime sleepiness and co-occurring nighttime insomnia in COMISA. DHx reduced activity in active phase (AP) and increased following activity in activity ending phase (AEP). This down-and-up activity response (DUR) by DHx was also observed in molecular clock deficient Cry1 and Cry2 double knockout mice (CryDKO) expressing nighttime activity rise under light-dark cycle (LD) and not observed in arrhythmic CryDKO under constant darkness (DD). When daytime timing hypoxia was exposed at transition from LD to DD, about every 6 h down and up and down wavelike activity responses appeared in arrhythmic CryDKO. Results indicate this wavelike response and AP activity overlap and cause DUR in rhythmic mice. DHx increased plasma corticosterone and this increase antagonized AP activity reduction by DHx. DHx reduced forebrain adenosine and morning adenosine inhibition by caffeine induced DUR. Adenosine inhibition by caffeine or istradefylline at transition from LD to DD induced wavelike response in CryDKO. It is possible that wavelike response is damped oscillation because, interestingly, chronic caffeine treatment induced circasemidian and/or circadian activity rhythms in arrhythmic CryDKO. Evening caffeine attenuated DUR by DHx, which suggested adenosine inhibition chronotherapy may improve OSA/COMISA symptoms. Our animal model will be useful to understand COMISA.