  We investigate the evolution of abundance of the asymmetric thermal Dark
Matter when its annihilation rate at chemical decoupling is boosted by the
Sommerfeld enhancement. Then we discuss the effect of kinetic decoupling on
relic abundance of asymmetric Dark Matter when the interaction rate depends on
the velocity. Usually the relic density of asymmetric Dark Matter is analyzed
in the frame of chemical decoupling. Indeed after decoupling from the chemical
equilibrium, asymmetric Dark Matter particles and anti--particles were still in
kinetic equilibrium for a while. It has no effect on the case of $s-$wave
annihilation since there is no temperature dependence in this case. However,
the kinetic decoupling has impacts for the case of $p-$wave annihilation and
Sommerfeld enhanced $s-$ and $p-$wave annihilations. We investigate in which
extent the kinetic decoupling affects the relic abundances of asymmetric Dark
Matter particle and anti--particle in detail. We found the constraints on the
cross section and asymmetry factor by using the observational data of relic
density of Dark Matter.
