© 2014, Springer-Verlag Berlin Heidelberg. Introduction: Obstructive sleep apnea (OSA) is a common disorder that is associated with impaired attention, memory and executive function. However, the mechanisms underlying such dysfunction are unclear. To determine the influence of sleep fragmentation and hypoxia, this study examined the effect of sleep fragmentation and hypoxia on cognition in OSA, while controlling for potentially confounding variables including sleepiness, age and premorbid intelligence. Method: Participants with and without OSA (N = 150) were recruited from the general community and a tertiary hospital sleep clinic. All underwent comprehensive, laboratory-based polysomnography (PSG) and completed assessments of cognition including attention, short- and long-term memory and executive function. Structural equation modelling (SEM) was used to construct a theoretically-driven model to examine the relationships between hypoxia and sleep fragmentation, and cognitive function. Results: Although after controlling for IQ, increased sleep disturbance was a significant predictor of decreased attention (p = 0.04) and decreased executive function (p = 0.05), controlling for age removes these significant relationships. No significant predictors of memory function were found. Conclusions: The mechanisms underlying the effects of OSA on cognition remain to be defined. Implications are discussed in light of these findings.