In this talk, we discuss local discontinuous Galerkin (LDG) method for solving the nonlinear time-dependent equations. The space discretization results in an extremely local, element based discretization, which is beneficial for adaptivity, parallel computing and maintaining high order accuracy on unstructured meshes. We also develop a novel semi-implicit time marching method. The method can be used in a large class of problems, especially for highly nonlinear ordinary differential equations (ODEs) without easily separating of stiff and non-stiff components, which is more general and efficient comparing with traditional semi-implicit methods. This time discretization method is intended to be combined with the method of lines, which provides a flexible framework to develop high order semi-implicit time marching methods for nonlinear partial differential equations (PDEs). Coupled with the LDG spatial discretization, the fully discrete schemes are all high order accurate in both space and time, and stable numerically with the time step proportional to the spatial mesh size. Using Lagrange multipliers the conditions imposed by the structure preserving limiters are directly coupled to a DG discretization combined with implicit time integration method. The structure preserving DG discretization is then reformulated as a Karush-Kuhn-Tucker (KKT) problem. We therefore develop an efficient active set semi-smooth Newton method that is suitable for the KKT formulation of time-implicit structure preserving DG discretizations. Convergence of this semi-smooth Newton method is proven using a specially designed quasi-directional derivative of the time-implicit structure preserving DG discretization. Numerical experiments are carried out to illustrate the accuracy and capability of the proposed method.