This　paper　focuses　on　the　Rayleigh-Taylor　instability　in　the　two-dimensional　system　of　equations　of　nonhomogeneous　incompressible　viscous　fluids　with　capillarity　effects　in　a　horizontal　periodic　domain　with　infinite　height.　First,　we　use　the　modified　variational　method　to　construct　(linear)　unstable　solutions　for　the　linearized　capillary　Rayleigh-Taylor　problem.　Then,　motivated　by　the　Grenier＇s　idea　in　(Grenier　in　Commun.　Pure　Appl.　Math.　53(9):1067-1091,　2000),　we　further　construct　approximate　solutions　with　higher-order　growing　modes　to　the　capillary　Rayleigh-Taylor　problem　and　derive　the　error　estimates　between　both　the　approximate　solutions　and　nonlinear　solutions　of　the　capillary　Rayleigh-Taylor　problem.　Finally,　we　prove　the　existence　of　escape　points　based　on　the　bootstrap　instability　method　of　Hwang-Guo　in　(Hwang　and　Guo　in　Arch.　Ration.　Mech.　Anal.　167(3):235-253,　2003),　and　thus　obtain　the　nonlinear　Rayleigh-Taylor　instability　result.　Our　instability　result　presents　that　the　Rayleigh-Taylor　instability　can　occur　in　the　fluids　with　capillarity　effects　for　any　capillary　coefficient　?　＞　0　if　the　critical　capillary　coefficient　is　infinite.　In　particular,　it　improves　the　previous　Zhang＇s　result　in　(Zhang　in　J.　Math.　Fluid　Mech.　24(3):70-23,　2022)　with　the　assumption　of　smallness　of　the　capillary　coefficient.