Background: Previous evidence suggests that slower gait speed is longitudinally associated with cognitive impairment, dementia and falls in older adults. Despite this, the longitudinal relationship between gait speed, cognition and falls in those with a diagnosis of dementia remains poorly explored. We sought to assess this longitudinal relationship in a cohort of older adults with mild to-moderate Alzheimer Disease (AD). Methods: Analysis of data from NILVAD, an 18-month randomised-controlled trial of Nilvadipine in mild to moderate AD. We examined: (i) the cross-sectional (baseline) association between slow gait speed and cognitive function, (ii) the relationship between baseline slow gait speed and cognitive function at 18 months (Alzheimer Disease Assessment Scale, Cognitive Subsection: ADAS-Cog), (iii) the relationship between baseline cognitive function and incident slow gait speed at 18 months and finally (iv) the relationship of baseline slow gait speed and incident falls over the study period. Results: Overall, one-tenth (10.03%, N = 37/369) of participants with mild-to-moderate AD met criteria for slow gait speed at baseline and a further 14.09% (N = 52/369) developed incident slow gait speed at 18 months. At baseline, there was a significant association between poorer cognition and slow gait speed (OR 1.05, 95% CI 1.01-1.09, p = 0.025). Whilst there was no association between baseline slow gait speed and change in ADAS-Cog score at 18 months, a greater cognitive severity at baseline predicted incident slow gait speed over 18 months (OR 1.04, 1.01-1.08, p = 0.011). Further, slow gait speed at baseline was associated with a significant risk of incident falls over the study period, which persisted after covariate adjustment (IRR 3.48, 2.05-5.92, p < 0.001). Conclusions: Poorer baseline cognition was associated with both baseline and incident slow gait speed. Slow gait speed was associated with a significantly increased risk of falls over the study period. Our study adds further evidence to the complex relationship between gait and cognition in this vulnerable group and highlights increased falls risk in older adults with AD and slow gait speed. Trial registration: Secondary analysis of the NILVAD trial (Clincaltrials.gov NCT02017340; EudraCT number 2012-002764-27). First registered: 20/12/2013.