The ageing process is characterised by declines in physical and cognitive function. However, the relationship between these trajectories remains a topic of investigation.Using four data waves collected triennially between ages 70 and 79, we tested for associations between multiple cognitive ability domains (verbal memory, processing speed, and visuospatial ability) and physical functions (walking speed, grip strength, and lung function). We firstly tested for associations between linear declines in physical and cognitive functions over the entire 9-year study period, and then, for lead-lag coupling effects between 3-year changes in cognitive and physical functions.Steeper linear decline in walking speed was moderately correlated with steeper linear declines in each cognitive domain. Steeper linear decline in grip strength was moderately correlated with steeper linear declines in verbal memory and processing speed. Lead-lag coupling models showed that decline in verbal memory was preceded by declines in walking speed and grip strength. By contrast, decline in grip strength was preceded by declines in processing speed and visuospatial ability, and decline in walking speed was preceded by decline in visuospatial ability. Following additional adjustment for covariates, only coupling effects from earlier decline in processing speed to later decline in grip strength remained significant (β = 0.545, p = 0.006).Our findings provide further evidence of an association between cognitive and physical declines and point to the potential order in which these changes occur. Decline in processing speed in particular may serve as a unique early marker of declining upper body strength.