This study investigated the relationship between neuropsychological test scores and gait speed in three gait tasks using baseline cross-sectional data from 4694 healthy adults (54% women, age (mean±sd) 62.4±8.2) from The Irish Longitudinal study on Aging (TiLDA). Global cognition, short term memory, speed of processing, executive function and sustained attention were measured by a detailed battery of neuropsychological tests. Gait speed was recorded from a GaitRite™ pressure sensing mat during a single walk and two dual walking tasks; dual cognitive walk (alternate letters) and dual motor walk (carrying a glass of water). Correlations between neuropsychological test scores and the three gait speed outcomes were investigated using univariate and multiple linear regressions models; firstly adjusting for age, gender, height, education and depression only and then including all neuropsychological test scores in the same regression model and adjusting as previously. It was found that short term memory, speed of processing and attention were significantly correlated with gait speed in all three gait conditions, with global cognition and executive function also significantly correlated with gait speed in the dual cognitive walk. The nature and complexity of the task performed affected gait speed with the addition of the cognitive task while walking causing a larger reduction in gait speed than the addition of the motor task. This indicates that for this healthy nationally representative population sample there is a link between neural processes involved in movement and cognition and this association differs depending on the gait task performed.