This paper deals with some results on commutative semigroups. We consider $(s,.)$ is externally commutative right zero semigroup is regular if it is intra regular and $(s,.)$ is externally commutative semigroup then every inverse semigroup is $u$–inverse semigroup. We will also prove that if $(S,.)$ is a $H$-semigroup then weakly cancellative laws hold in $H$-semigroup. In one case we will take $(S,.)$ is commutative left regular semigroup and we will prove that $(S,.)$ is $\Pi$-inverse semigroup. We will also consider $(S,.)$ is commutative weakly balanced semigroup and then prove every left (right) regular semigroup is weakly separate, quasi separate and separate. Additionally, if $(S,.)$ is completely regular semigroup we will prove that $(S,.)$ is permutable and weakly separative. On a concluding note we will show and prove some theorems related to permutable semigroups and GC commutative Semigroups.