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To examine the association between sleep architecture, sleep-disordered breathing, and cognition in older men.Population-based cross-sectional study.Six clinical sites in the United States.Two thousand nine hundred nine community-dwelling men aged 67 and older who were not selected on the basis of sleep problems or cognitive impairment.Predictors were measured using in-home polysomnography: sleep architecture, nocturnal hypoxemia (any sleep time with arterial oxygen saturation <80%), apnea–hypopnea index (AHI), and arousal index. Cognitive outcomes were measured using the modified Mini-Mental State Examination (3MS), Trail-Making Test Part B (TMT-B), and the Digit Vigilance Test (DVT).Analyses adjusted for age, race, education, body mass index, lifestyle, comorbidities, and medication use showed that participants who spent less percentage of time in rapid eye movement (REM) sleep had lower levels of cognition; participants in the lowest quartile (<14.8%) took an average of 5.9 seconds longer on the TMT-B and 20.1 seconds longer on the DVT than those in the highest quartile (≥23.7%). Similarly, greater percentage of time spent in Stage 1 sleep was related to poorer cognitive function. Participants in the highest quartile of Stage 1 sleep (≥8.6%) had worse cognitive scores on average than those in the lowest quartile (<4.0%). Those with nocturnal hypoxemia took an average of 22.3 seconds longer to complete the DVT than those without, but no associations were found with 3MS or the TMT-B.Spending less percentage of time in REM sleep and greater percentage of time in Stage 1 sleep and having higher levels of nocturnal hypoxemia were associated with poorer cognition in older men. Further studies are needed to clarify the direction of these associations and to explore potential mechanisms.