Functionally　graded　material　(FGM)　is　a　promising　heat　insulation　material.　Wave　propagation　in　FGM　structures　has　received　much　attention　for　the　purpose　of　non-destructive　testing　and　evaluation.　Few　literatures　dealt　with　the　thermoelastic　wave　in　FGM　structures　although　the　thermal　effect　would　cause　attenuations　of　elastic　waves.　In　this　paper,　guided　thermoelastic　waves　in　FGM　plates　subjected　to　stress-free,　isothermal　boundary　conditions　are　investigated　in　the　context　of　the　Green-Lindsay　(GL)　generalized　thermoelastic　theories　(with　two　relaxation　times).　Coupled　wave　equations　and　heat　conduction　equation　are　solved　by　the　Legendre　polynomial　approach.　Dispersion　curves　for　a　pure　elastic　graded　plate　are　calculated　to　make　a　comparison　with　the　published　data.　For　the　thermoelastic　graded　plate,　dispersion　curves　of　thermal　modes　and　elastic　modes　are　illustrated　simultaneously.　Attenuation　curves　for　graded　plates　with　different　relaxation　times　are　compared.　The　influences　of　different　material　gradient　shapes　are　discussed.　Two　homogeneous　thermoelastic　plates　with　different　volume　fractions　are　obtained　to　show　their　differences　from　graded　plates.　Finally,　thermoelastic　wave　dispersion　curves　for　a　homogeneous　plate　and　a　graded　plate　are　calculated　in　the　context　of　the　classical　coupled　thermoelastic　theory　(CT)　to　show　its　differences　and　similarities　to　the　generalized　theory.　(C)　2010　Elsevier　Ltd.　All　rights　reserved.