In this paper we establish the nonlinear stability of shock waves for viscous conservation laws. It Is shown that when the Initial data Is a perturbation of viscous shock waves, then the solution converges to viscous shock waves, properly translated, as time tends to Infinity. The perturbation Is not assumed to be weak compared to the viscous shock waves. Our analysis Is based on the following two Ideas, both motivated by physical considerations: First, we decompose the general solution Into viscous shock waves, linear and nonlinear diffusion waves, and an error term. The error term carries zero net flow of the basic dependent variables. The idea originated from the realization that the sytem is conservative, and a general solution Is eventually separated Into normal modes. The construction of diffusion waves Is based on self-similar solutions for Burgers equation and the heat equation. Our second Idea consists of a new combination of the characteristic method and the energy method. The energy method is a standard technique for parabolic systems. The reason for using a standard technique for studying hyperbolic systems, the characteristic method, Is that although our system is parabolic, the solutions should be classified physically as hyperbolic waves due to nonlinear effects.