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This paper studies differential games with age-structured state variables, where the state depends on both time and an age variable representing cohorts, durations, or maturity classes. We propose tools for constructing approximate Nash equilibria under dual closed-loop information structures. A verification theorem is established that allows one to check whether a given strategy profile constitutes such an approximate equilibrium. This theorem does not require the regularity assumptions typically imposed by standard optimal control techniques, which are often not satisfied in games. Our main result establishes conditions under which these dual $\varepsilon$-Nash equilibria are equivalent to classical closed-loop $\varepsilon$-Nash equilibria. This provides a practical verification criterion for determining when a strategy profile is indeed a closed-loop $\varepsilon$-Nash equilibrium in the original age-structured game.