It can be argued that the Lin-Dadarlat-Eilers stable uniqueness theorem is one of the main driving forces behind several recent landmark results related to the classification program for nuclear C*-algebras. In a nutshell, the theorem strengthens the Cuntz picture of bivariant K-theory, and translates a KK-theoretic assumption into a rather strong statement involving (stable) asymptotic unitary equivalence of *-homomorphisms, which becomes immensely useful for extracting the role of K-theory in classification. In this talk I will present a generalization of the stable uniqueness theorem to the setting of C*-dynamical systems over a given locally compact group. I will also explain why this should be expected to be important in the context of classifying C*-dynamics up to cocycle conjugacy.