A living cell deforms or flows in response to mechanical stresses. A recent report shows that dynamic mechanics of living cells depends on the timescale of mechanical loading, in contrast to the prevailing view of some authors that cell rheology is timescale-free. Yet the molecular basis that governs this timescale-dependent behavior is elusive. Using molecular dynamics simulations of protein-protein noncovalent interactions, we show that multipower laws originate from a nonequilibrium-to-equilibrium transition: when the loading rate is faster than the transition rate, the power-law exponent alpha(1) is weak; when the loading rate is slower than the transition rate, the exponent alpha(2) is strong. The model predictions are confirmed in both embryonic stem cells and differentiated cells. Embryonic stem cells are less stiff, more fluidlike, and exhibit greater alpha(1) than their differentiated counterparts. By introducing a near-equilibrium frequency f(eq), we show that all data collapse into two power laws separated by f/f(eq), which is unity. These findings suggest that the timescale-dependent rheology in living cells originates from the nonequilibrium-to-equilibrium transition of the dynamic response of distinct, force-driven molecular processes.