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In this paper we propose asymptotic consistent exponential-type integrators for the Klein-Gordon-Schrodinger system. This novel class of integrators allows us to solve the system from slowly varying relativistic up to challenging highly oscillatory non-relativistic regimes without any step size restriction. In particular, our first- and second-order exponential-type integrators are asymptotically consistent in the sense of asymptotically converging to the corresponding decoupled free Schrodinger limit system.

Asymptotic consistent exponential-type integrators for Klein-Gordon-Schrödinger systems from relativistic to non-relativistic regimes