In old age, cognitive and physical functions are correlated. Knowing the correlations between genetic and environmental influences underlying this correlation can help to clarify the reasons for the observable (phenotypic) correlation. We estimated these correlations in a sample of 1,053 pairs of twins from the Longitudinal Study of Aging Danish Twins. Cognitive function was measured using forward and backward digit span, immediate and delayed memory, and fluency tasks. Physical function was measured using self-report of ability to carry out physical activities including walking, running, and climbing stairs. The phenotypic correlation between latent variable representations was .46 (95% confidence interval 0.27-0.65). The genetic correlation was .56 (95% confidence interval 0.15-1.00) and the nonshared environmental correlation .48 (95% confidence interval 0.35-0.61). We discuss several ways of interpreting these correlations.