The relationship amongst state-redundancy and time consistency of differential games is investigated. A class of state-redundant games is detected, where the state dynamics and the payoff functions of all players are additively separable w.r.t. control variables. We prove that, in this class of games, open-loop Nash and degenerate feedback Stackelberg equilibria coincide, both being subgame perfect. This allows us to bypass the issue of the time inconsistency that typically affects the open-loop Stackelberg solution.