  We investigate the evolution of the abundance of the asymmetric thermal Dark
Matter when its annihilation rate at chemical decoupling is boosted by the
Sommerfeld enhancement. We perform the detailed analysis of the effect of $s$--
and $p$--wave Sommerfeld enhanced annihilation cross section on the relic
abundances of asymmetric Dark Matter particle and anti--particle both in
numerical and analytical way. The constraints on the coupling and asymmetric
factor are given by using the observational data of the relic density of Dark
Matter.
