In the paper we describe the least Clifford congruence  on an idempotent-surjective R-semigroup, and so we generalize the result of LaTorre (1983). In addition, a characterization of all Clifford congruences on such a semigroup (in particular, on a structurally regular semigroup) is given. Furthermore, we nd necessary and sufcient conditions for  to be idempotent pure or E-unitary. Moreover, using some earlier result, we give a description of all USG-congruences on an idempotent-surjective semigroup, and so we generalize the result of Howie and Lallement for regular semigroups (1966). Finally, in Section 4 we study the subdirect products of an E-unitary semigroup and a Clifford semigroup.