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.