In a number of earlier papers the study of the structure of semigroups has been approached by means of right congruences. Such n approach seems appropriate since a right congruence is one of the possible analogs of both the right ideal of a ring and the subgroup in a group. Each of these substructures plays a strong role in the study of the structure of their respective systems. in both the ring and the group the internal direct product is nat-urally and effectively defined. however what such an internal direct product should be for two right congruences of a semigroup is not so clear. In this paper we will offer a possible definition and consider some of the consequences of it. We will also extend some of these results to automata.