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We show that the posemigroup dominion of a commutative posemigroup is again a commutative posemigroup and all varieties of commutative posemigroups are epimorphically closed. Next, we show that certain subvarieties of the variety of all commutative posemigroups are saturated. Finally, we show that a commutative posemigroup S is saturated if S k is saturated for some positive integer k. [ABSTRACT FROM AUTHOR]