The group congruences on an eventually regular ($\pi$-regular) semigroups is described in [5]. In this paper, by the method from [5], we give some new descriptions for group congruences. Also, we consider normal congruences on a semigroup which is generated by all the idempotents from a $\pi$-regular semigroup. If $S$ is a regular semigroup and idempotents of $S$ form a left zero band, then we define the normal congruence pair and by it we describe some congruences. For the related results see [7].