This paper describes the conjunctive counterpart of De Boeck and Rosenberg's hierarchical classes model. Both the original model and its conjunctive counterpart represent the set-theoretical structure of a two-way two-mode binary matrix. However, unlike the original model, the new model represents the row-column association as a conjunctive function of a set of hypothetical binary variables. The conjunctive nature of the new model further implies that it may represent some conjunctive higher order dependencies among rows and columns. The substantive significance of the conjunctive model is illustrated with empirical applications. Finally, it is shown how conjunctive and disjunctive hierarchical classes models relate to Galois lattices, and how hierarchical classes analysis can be useful to construct lattice models of empirical data.