The aim of this study was to determine the cognitive deficits that accompany different levels of severity of obstructive sleep apnea–hypopnea syndrome (OSAHS). The sample originally consisted of 71 adult male volunteers with at least 11 years of education. Participants were assigned to groups based on their apnea–hypopnea index (AHI). There were 20 participants in the mild-to-moderate OSAHS group (AHI 6–28; mean age 41.8 ± 8.96 years), 16 in the severe OSAHS group (AHI 38–86; mean age 44.5 ± 7.96 years), and 35 in the non-OSAHS group (AHI 0–3; mean age 41.8 ± 8.96 years). Neuropsychological functions were measured using Stroop Test TBAG version, Cancellation Test, Auditory Verbal Learning Test, Serial Digit Learning Test, and Raven Standard Progressive Matrices. Analyses were conducted on z-transformed scores. Multivariate analysis of variance (education as covariate) showed decrease in various functions such as processing speed, disturbance in selective and sustained attention, deficit in visual perception, search and scan, deficit in recognition memory, increase in susceptibility to interference, and decrease in visuospatial reasoning and general ability. Correctness of estimation increased as severity of OSAHS increased. However, principal component analysis showed that OSAHS severity represents impairment in the basic processes of processing speed and vigilance/sustained attention. Untreated OSAHS patients are potential risks to themselves and to others. Controlled studies are necessary for unraveling the functional correlates of OSAHS.