Semigroups satisfying some type of generalized commutativity were considered in quite a number of papers. S. Lajos, A. Nagy and M. Yamada dealed with externally commutative semigroups. N. Stevanović and P. V. Protić in [Structure of weakly externally commutative semigroups, Algebra Colloq. 13:3 (2006) 441-446], introduced the notion of weakly externally commutative semigroup and gave a structural description for some subclasses of this class of semigroups. In this paper we consider a class which is a generalization of the class of externally commutative semigroups.