The scope of the present paper is to develop a formal system of assertoric categorical syllogism (abridged as "CS") and to discuss some problems connected with it. By this an improvement in the Thomistic statement of the theory is aimed at. Such an improvement seems to be needed for two reasons: (1) considerable progress has been achieved in formal logic in recent times; but many leading logicians being only slightly interested in CS and most Thomists having no knowledge at all of recent formal logic, these achievements are seldom applied to the traditional doctrine and, if they are, the applications are not known; (2) some objections have been raised against the traditional theory of CS which need to be examined on a more rigorous basis.