Abstract. We define a framework to reason about implementations of equational theories in the presence of an adaptive adversary. We particularly focus on soundess of static equivalence. We illustrate our framework on several equational theories: symmetric encryption, XOR, modular exponentiation and also joint theories of encryption and modular exponentiation. This last example relies on a combination result for reusing proofs for the separate theories. Finally, we define a model for symbolic analysis of dynamic group key exchange protocols, and show its computational soundness.