We　investigate　the　stabilizing　effects　of　the　magnetic　fields　in　the　linearized　magnetic　Rayleigh–Taylor　(RT)　problem　of　a　nonhomogeneous　incompressible　viscous　magnetohydrodynamic　fluid　of　zero　resistivity　in　the　presence　of　a　uniform　gravitational　field　in　a　three-dimensional　bounded　domain,　in　which　the　velocity　of　the　fluid　is　non-slip　on　the　boundary.　By　adapting　a　modified　variational　method　and　careful　deriving　a　priori　estimates,　we　establish　a　criterion　for　the　instability/stability　of　the　linearized　problem　around　a　magnetic　RT　equilibrium　state.　In　the　criterion,　we　find　a　new　phenomenon　that　a　sufficiently　strong　horizontal　magnetic　field　has　the　same　stabilizing　effect　as　that　of　the　vertical　magnetic　field　on　growth　of　the　magnetic　RT　instability.　In　addition,　we　further　study　the　corresponding　compressible　case,　i.e.,　the　Parker　(or　magnetic　buoyancy)　problem,　for　which　the　strength　of　a　horizontal　magnetic　field　decreases　with　height,　and　also　show　the　stabilizing　effect　of　a　sufficiently　large　magnetic　field.　©　2015,　Springer　Basel.