  In this paper we discuss the local discontinuous Galerkin methods coupled
with two specific explicit-implicit-null time discretizations for solving
one-dimensional nonlinear diffusion problems $U_t=(a(U)U_x)_x$. The basic idea
is to add and subtract two equal terms $a_0 U_{xx}$ on the right hand side of
the partial differential equation, then to treat the term $a_0 U_{xx}$
implicitly and the other terms $(a(U)U_x)_x-a_0 U_{xx}$ explicitly. We give
stability analysis for the method on a simplified model by the aid of energy
analysis, which gives a guidance for the choice of $a_0$, i.e, $a_0 \ge
\max\{a(u)\}/2$ to ensure the unconditional stability of the first order and
second order schemes. The optimal error estimate is also derived for the
simplified model, and numerical experiments are given to demonstrate the
stability, accuracy and performance of the schemes for nonlinear diffusion
equations.
