Abstract This article deals with the question of the attribution of criminal responsibility to leaders of large criminal organizations for crimes which were committed by their subordinates in compliance with their orders. It presents a critical assessment of Roxin’s theory of indirect perpetration through an organized apparatus of power, as well as of the International Criminal Court’s theory of indirect co-perpetration through an organized structure of power. Both theories have serious shortcomings and, in addition, fail to conceptually capture the greater responsibility of the leaders of the organization vis-à-vis the executors. Thus, this article presents an outline of a typological system of the influence over the crime, which constitutes an alternative system of criminal participation and offers a better solution to the problem of criminal responsibility of the members of an organized apparatus of power.