  In this paper, we study the asymptotic behaviors of finite energy solutions
to the Landau-Lifshitz flows from $\Bbb R^2$ into K\"ahler manifolds. First, we
prove that the solution with initial data below the critical energy converges
to a constant map in the energy space as $t\to \infty$ for the compact
Riemannian surface targets. In particular, when the target is a two dimensional
sphere, we prove that the solution to the Landau-Lifshitz-Gilbert equation with
initial data having an energy below $4\pi$ converges to some constant map in
the energy space. Second, for general compact K\"ahler manifolds and initial
data of an arbitrary finite energy, we obtain a bubbling theorem analogous to
the Struwe's results on the heat flows.
