Experimental and computational dynamic force spectroscopy is widely used to determine the mechanical properties of single biomolecules. Whereas so far the focus has mainly been on rupture or unfolding forces, recent force-probe molecular dynamics simulations have revealed a strong loading rate dependence of biomolecular elasticities, which cannot be explained by the established one-dimensional transition-state treatments. We show that this nonequilibrium behavior can be explained by a theory that includes relaxation effects. For three structurally and mechanically quite diverse systems, a single relaxation mode suffices to quantitatively describe their loading-rate-dependent elastic behavior. Atomistic simulations of these systems revealed the microscopic nature of the respective relaxation modes. This result suggests a new type of "elasticity spectroscopy" experiment, which should render nonequilibrium properties of structured macromolecules accessible to single-molecule force spectroscopy.