Musculoskeletal disorders are common among older people. Preventive strategies require understanding of age-related changes in strength, function and body composition, including how they interrelate. We have described, and examined associations between, 9-year changes in these parameters among 2917 Health, Aging and Body Composition Study participants (aged 70-79 years). Appendicular lean mass (ALM), whole body fat mass and total hip BMD were ascertained using DXA; muscle strength by grip dynamometry; and muscle function by gait speed. For each characteristic annualised percentage changes were calculated; measures of conditional change (independent of baseline) were derived and their interrelationships were examined using Pearson correlations; proportion of variance at 9-year follow-up explained by baseline level was estimated; and mean trajectories in relation to age were estimated using linear mixed models. Analyses were stratified by sex. Median [lower quartile, upper quartile] annual percentage declines were grip strength (1.5 [0.0, 2.9]), gait speed (2.0 [0.6, 3.7]), ALM (0.7 [0.1, 1.4]), fat mass (0.4 [− 1.1, 1.9]) and hip BMD (0.5 [0.0, 1.1]). Declines were linear for ALM and accelerated over time for other characteristics. Most conditional change measures were positively correlated, most strongly between ALM, fat mass and hip BMD (r > 0.28). Proportion of variation at follow-up explained by baseline was lower for grip strength and gait speed (39-52%) than other characteristics (69-86%). Strength and function declined more rapidly, and were less correlated between baseline and follow-up, than measures of body composition. Therefore, broader intervention strategies to prevent loss of strength and function in later life are required as those targeting body composition alone may be insufficient.