  We show results of simulations of a weakly driven four dimensional Edwards-
Anderson spin glass, which presents clear signatures of dynamical
ultrametricity at low temperatures. The presence of a hierarchical organization
of time scales is evident from the appearance of a triangular relation between
correlations at three characteristic long times in the asymptotic limit of
small drive, and also in the scaling form of stationary correlations in this
regime. The differences between this scenario and known results of the aging
dynamics of the model are also analyzed.
