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We report nonequilibrium magnetodynamics in the Rashba-superconductor GeTe, which lacks inversion symmetry in the bulk. We find that at low temperature the system exhibits a nonequilibrium state, which decays on timescales that exceed conventional electronic scattering times by many orders of magnitude. This reveals a nonequilibrium magnetoresponse that is asymmetric under magnetic-field reversal and, strikingly, induces a nonequilibrium superconducting state distinct from the equilibrium one. We develop a model of a Rashba system in which nonequilibrium configurations relax on a finite timescale that captures the qualitative features of the data. We also obtain evidence for the slow dynamics in another nonsuperconducting Rashba system. Our work provides insights into the dynamics of noncentrosymmetric superconductors and Rashba systems in general.