The following coupled damped Klein-Gordon-Schrödinger equations are considered iψt + κψxx + iαb(x)ψ = φψχ(ω), φtt − φxx + φ + λ(x)φt = −Reψxχ(ω), where Ω is a bounded domain of R, with smooth boundary Γ and ω is a neighbourhood of ∂Ω satisfying the geometric control condition. The aim of the paper is to prove the existence, uniqueness and uniform decay for the solutions following the ideas presented in the works of [1] and [2]. Mathematics Subject Classification (2010). 35B40, 35B45, 35Q55.