  Let $(M,\overline{g})$ be a K\"ahler surface, and $\Sigma$ an immersed
surface in $M$. The K\"ahler angle of $\Sigma$ in $M$ is introduced by
Chern-Wolfson \cite{CW}. Let $(M,\overline{g}(t))$ evolve along the
K\"ahler-Ricci flow, and $\Sigma_t$ in $(M,\overline{g}(t))$ evolve along the
mean curvature flow. We show that the K\"ahler angle $\alpha(t)$ satisfies the
evolution equation: $$ (\frac{\partial}{\partial
t}-\Delta)\cos\alpha=|\overline\nabla
J_{\Sigma_t}|^2\cos\alpha+R\sin^2\alpha\cos\alpha, $$ where $R$ is the scalar
curvature of $(M, \overline{g}(t))$.
  The equation implies that, if the initial surface is symplectic (Lagrangian),
then along the flow, $\Sigma_t$ is always symplectic (Lagrangian) at each time
$t$, which we call a symplectic (Lagrangian) K\"ahler-Ricci mean curvature
flow.
  In this paper, we mainly study the symplectic K\"ahler-Ricci mean curvature
flow.
