Many studies have reported that impaired gait precedes cognitive impairment in older people. We aimed to characterise the time course of cognitive and motor decline in older individuals and the association of these declines with the pathologies of Alzheimer's disease and related dementias. This multicohort study used data from three community-based cohort studies (Religious Orders Study, Rush Memory and Aging Project, and Minority Aging Research Study, all in the USA). The inclusion criteria for all three cohorts were no clinical dementia at the time of enrolment and consent to annual clinical assessments. Eligible participants consented to post-mortem brain donation and had post-mortem pathological assessments and three or more repeated annual measures of cognition and motor functions. Clinical and post-mortem data were analysed using functional mixed-effects models. Global cognition was based on 19 neuropsychological tests, a hand strength score was based on grip and pinch strength, and a gait score was based on the number of steps and time to walk 8 feet and turn 360°. Brain pathologies of Alzheimer's disease and related dementias were assessed at autopsy. From 1994 to 2022, there were 1570 eligible cohort participants aged 65 years or older, 1303 of whom had cognitive and motor measurements and were included in the analysis. Mean age at death was 90·3 years (SD 6·3), 905 (69%) participants were female, and 398 (31%) were male. Median follow-up time was 9 years (IQR 5-11). On average, cognition was stable from 25 to 15 years before death, when cognition began to decline. By contrast, gait function and hand strength declined during the entire study. The combinations of pathologies of Alzheimer's disease and related dementias associated with cognitive and motor decline and their onsets of associations varied; only tau tangles, Parkinson's disease pathology, and macroinfarcts were associated with decline of all three phenotypes. Tau tangles were significantly associated with cognitive decline, gait function decline, and hand function decline (p<0·0001 for each); however, the association with cognitive decline persisted for more than 11 years before death, but the association with hand strength only began 3·57 years before death and the association with gait began 3·49 years before death. By contrast, the association of macroinfarcts with declining gait function began 9·25 years before death (p<0·0001) compared with 6·65 years before death (p=0·0005) for cognitive decline and 2·66 years before death (p=0·024) for decline in hand strength. Our findings suggest that average motor decline in older adults precedes cognitive decline. Macroinfarcts but not tau tangles are associated with declining gait function that precedes cognitive decline. This suggests the need for further studies to test if gait impairment is a clinical proxy for preclinical vascular cognitive impairment. National Institutes of Health.