Withtheadventofleft-handedmagneticmaterials,itisdesirabletodevelophigh-performancewavedevicesbasedontheirnovelpropertiesofwavepropagation.Thisletterreportsthespecialpropertiesofelasticwavepropagationinmagnetoelasticmultilayeredcompositeswithnegativepermeabilityascomparecdtothoseincounterpartstructureswithpositlvepermeability.Thesenovelpropertiesofelasticwavesarediscernedfromthepersifieddispersioncurves,whichrepresentthepropagationandattenuationcharacteristicsofelasticwaves.Tocomputethesedispersioncurves,themethodofreverberation-raymatrixisextendedfortheanalysisofelasticwavesinmagnctoelasticmultilayeredcomposites.Althoughonlytheresultsofasinglepiezomagneticandabinarymagnetoelasticlayerswithmechanicallyfreeandmagneticallyshortsurfacesaswellaspelrfectinterfaceareillustratedinthenumericalexamples,theanalysisisapplicablelomagnetoelasticmultilayeredstructureswithotherkindsofboundaries/interfaces.