We evaluated the influence of untreated obstructive sleep apnoea (OSA) on the magnitude of cognitive decline and on several cognitive subdomains in patients with mild to moderate Alzheimer's Disease (AD).In this single-centre study, 144 patients were recruited prospectively from a cognitive impairment unit and underwent overnight polysomnography.The mean (sd) change in the Alzheimer's Disease Assessment Scale cognitive subscale (ADAS-cog) score at 12 months was 3.19 (5.61) in the non-OSA group and 0.08 (5.62) in the OSA group, with an intergroup difference of -3.36 (95%CI 0.19 to 0.16; p=0.002). We did not observe a significant difference in any cognitive subdomains at 12 months. Regarding Mini-Menatl State Examination scores at 36 months, the mean change was 1.69 (95%CI -1.26 to 4.64; p=0.445). No significant differences were found among different OSA severity groups.We observed that ADAS-cog scores were better in the OSA group than in the non-OSA group by a statistically but not clinically significant margin. We did not find differences in the different cognitive subdomains after 1 year or in global cognition after 3 years of follow-up.