We　investigate　the　instability　and　stability　of　some　steady-states　of　a　three-dimensional　nonhomogeneous　incompressible　viscous　flow　driven　by　gravity　in　a　bounded　domain　Omega　of　class　C-2.　When　the　steady　density　is　heavier　with　increasing　height　(i.e.,　the　Rayleigh-Taylor　steady-state),　we　show　that　the　steady-state　is　linear　unstable　(i.e.,　the　linear　solution　grows　in　time　in　H-2)　by　constructing　a　(standard)　energy　functional　and　exploiting　the　modified　variational　method.　Then,　by　introducing　a　new　energy　functional　and　using　a　careful　bootstrap　argument,　we　further　show　that　the　steady-state　is　nonlinear　unstable　in　the　sense　of　Hadamard.　When　the　steady　density　is　lighter　with　increasing　height,　we　show,　with　the　help　of　a　restricted　condition　imposed　on　steady　density,　that　the　steady-state　is　linearly　globally　stable　and　nonlinearly　asymptotically　stable　in　the　sense　of　Hadamard.　(C)　2014　Elsevier　Inc.　All　rights　reserved.