Sleep-disordered breathing (SDB) has been associated with neuropsychological (NP) deficits. The extent to which such effects are attributable to unmeasured confounders or selection biases, or are manifest across a range of SDB is unclear. The relationship of SDB with a broad range of NP functions was examined in 100 volunteers with a spectrum of SDB and without underlying comorbidity. Factor analysis suggested that the NP tests could be summarized as four constructs: declarative memory, signal discrimination, working memory, and set shifting. These factors plus vigilance were dependent variables. Independent variables were age, the respiratory disturbance index (RDI), a sleepiness score, the arousal index, and sleep-associated hypoxemia. Factors “declarative memory” (measuring 25% of the common variance, � � 0.95), “signal discrimination” (10% variance, � � 0.70), and “working memory” (9% variance, � � 0.52) were each significantly, linearly predicted by hypoxemia and/or the RDI, with no evidence for significant threshold effects. SDB measures accounted for 4‐6% of the variance in NP constructs. In contrast, sleepiness best predicted vigilance. Thus, adverse exposures (hypoxemia or RDI) during sleep may negatively influence NP functions in a dose‐response relationship, and, other than vigilance, these effects may not be directly attributable to sleepiness. Obstructive sleep apnea hypopnea syndrome (OSAHS) is the health condition most commonly associated with disordered breathing during sleep and sleep fragmentation. A major component of the morbidity of the condition is thought to relate to short-term and possible long-term neurocognitive deficits caused by exposure to intermittent hypoxemia, hypercapnia, and arousal, acting independently or synergistically. Deficits have been examined using classic neuropsychological (NP) approaches with administration of test batteries that assess a range of functions (broadly considered to assess different structural areas of the brain). These include executive functions (processes involved in planning, initiation, or self-regulation of goal-oriented behavior), attention (including span of apprehension, sustained attention, vigilance, information processing efficiency, and response times), and learning and memory. Interpretation of such tests requires careful consideration of the noncognitive influences that may confound study findings, including the sensitivity of the tests to the effects of age, alcohol consumption, education level, and motivation, as well as differences in baseline intelligence. Studies that have used these approaches to assess NP function in OSAHS include case series of patients with comparisons with published normative data (1), case‐control and cross-sectional studies (2, 3), pre‐poststudies (4, 5), small randomized control studies (6, 7), and a population-based study (8). A wide range of results that could be attributable to the effects of OSAHS (or to the effects of treatment aimed at reversing OSAHS) has been reported. In general, the largest and broadest range of NP deficits has been demonstrated in studies of patients with severe SDB, as evidenced by pathological levels of sleepiness, severe sleep-associated hypoxemia, and/or with RDIs � 40 (1, 2, 4, 9). Study results suggest that hypoxemia most closely predicts deficits in executive functions and psychomotor skills, whereas sleepiness predicts deficits in attention measures (3, 5). However, it is not clear from these studies if effects were due to unmeasured confounding (from studying subjects with underlying medical or psychological problems) and whether effects persisted across the entire spectrum of SDB. This study is unique in that it includes a large number of subjects with low to intermediate levels of SDB, most of whom were not referred to a Sleep Center, and whom were also screened to be free of underlying neurological or medical problems that might impact NP function. This study assesses the extent to which variations in NP function in a nonreferred sample may be associated with variations in sleepiness, as described by both objective and subjective measures, and by direct measures of SDB, that is, indices of sleep-related hypoxemia, sleep fragmentation, and the RDI.