  The smoothing effect of the Cauchy problem for a class of kinetic equations
is studied. We firstly consider the spatially homogeneous non linear Landau
equation with Maxwellian molecules and inhomogeneous linear Fokker-Planck
equation to show the ultra-analytic effects of the Cauchy problem. Those
smoothing effect results are optimal and similar to heat equation. In the
second part, we study a model of spatially inhomogeneous linear Landau equation
with Maxwellian molecules, and show the analytic effect of the Cauchy problem.
