Each non-normal intuitionistic modal logic is obtained by translating the intuitionistic language into modal language and by conjoining the S4 axioms for one primitive modal operator with the axioms of the non-normal modal system for another primitive operator, adding to this connecting axioms for the two operators. Algebraic methods are used to prove that the resulting systems are complete with respect to a type of model in which there are two accessibility relations, one for the S4 operator and another for the non-normal operator. The paper presumes acquaintance with the author's earlier paper in Italian studies in the philosophy of science, Boston Stud. Philos. Sci., Vol. 47, 59--72 (1981; Zbl 0452.03014).