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Background,Motivation and Objective Recently,phononie crystals consisting of two alternating solid or fluid constituents which can exhibit band gaps (BG) in their transmission spectra have been attracted much attention because they have the capability to realize the perfect mirrors,confinement of acoustic energy in defect modes and the fabrication of very efficient wave guide.Magnetoelectric composite materials have magneto-electric coupling effects,which can facilitate the energy conversion among magneticity,electricity,and mechanics without other devices.In this paper we analyze the Rayleigh wave propagation in layered periodic magnetoelectric structures.The analytical method and the results can be useful for the design of novel acoustic wave devices.