Abstract We prove the existence of positive ground states for the nonlinear Schrödinger system { − Δ u + ( 1 + a ( x ) ) u = F u ( u , v ) + λ v , − Δ v + ( 1 + b ( x ) ) v = F v ( u , v ) + λ u , where a, b are periodic or asymptotically periodic and F satisfies some superlinear conditions in ( u , v ) . The proof is based on the method of Nehari manifold and the concentration-compactness principle. MSC:35J05, 35J50, 35J61.