In present work, we conduct a statistical analysis of age-related changes in the neuromuscular system of healthy subjects. The experiment involved 29 volunteers who were assigned to different age groups: 20–24 years old, 64–69 years old and 75–90 years old. Within the framework of the Memory Functions Formalism, a quantitative assessment of the statistical memory effects and relaxation times for the dynamometric signals of the subjects recorded at different force impulses was performed. We have found that the dynamics of force signals of volunteers of the second and third groups is characterized by shorter lifetimes of statistical memory, as well as a transition from periodic to more probabilistic behavior. The calculated relaxation times for the subjects from older age groups were 2–3 times higher than those for young volunteers. An analysis of the spectral behavior of the temporal correlation function and memory functions allows establishing additional age-related changes in human hand-eye coordination. The presented results will be of interest to specialists in the field of biophysics, physics of complex systems, as well as neurosciences and gerontology.