We investigate dynamical systems of gauge symmetric Ising spin glasses usingthe method of the gauge transformation. Several exact relations are derived among dynamicalquantities such as the equilibrium auto-correlation function and the non-equilibrium remanentmagnetization. The same result as in the static case is obtained in terms of the equivalence of theferromagnetic and the spin glass order if the temperature and the randomness satisfy a specialcondition (Nishimori line). An exact equivalence of non-equilibrium relaxations in the spin glassphase is derived between the remanent magnetization evolved from the strong field limit and theauto-correlation function from a supercooled state. We also have a plausible argument for theabsence of re-entrant transition.