We　investigate　quantum　nonlocality　dynamics　of　a　three-level　atom　and　a　class　of　two-mode　non-classical　states　(including　the　entangled　coherent　state,　the　pair　coherent　state　and　the　two-mode　squeezed　state)　in　the　non-degenerate　two-photon　Jaynes-Cummings　model.　It　is　shown　that　the　time　evolution　of　the　Bell　nonlocality　for　the　case　of　the　entangled　coherent　state　is　closely　related　to　the　average　number　of　photons　in　the　two-mode　field.　For　the　cases　of　the　pair　coherent　state　and　the　two-mode　squeezed　state,　the　effect　of　Bell　nonlocality　sudden　death　is　demonstrated,　and　the　absolute　value　of　the　＜　B(CHSH)＞　exhibits　exact　periodic　collapses　and　revivals.