The aim of this paper is to study the acoustic propagatorHin a perturbed multistratified domain Ω with the conjugate operator method.Hdenotes the self-adjoint operator −∇c(x)∇ inL2(Ω) with a Dirichlet condition at the boundary ∂Ω. Herecdenotes the propagation velocity depending on the nature of the stratification of Ω. We shall give some spectral properties ofHand we establish the limiting absorption principle in an optimal scale of Besov spaces.