Let NSET be the category of enumerated sets. I n the ER&OV book [l] a lot has been said about the following problems related to this category. Let S, , S, be two enumerated sets. What assumptions about these sets should we accept in order to find "good" (i.e. principal computable) enumeration of the set NSET(S, , S,) of all NSETmorphism from S, into S,! What are the properties of enumerated sets of NSETmorphisms obtained in this way! These questions lead to very deep and subtle considerations. The obtained results have a local character, naturally. It is possible, however, to raise questions of more global character. Let A be an arbitrary non-empty enumerated set. With what assumptions about A it is possible, in a functorial way, to enumerate a t once all the sets NSET(A, S ) for all enumerated sets S? What are the properties of hom-functors obtained in this way? I n this paper we answer these questions with an additional requirement that the considered hom-functors be distributive (or even constructive). The notions of distributive and constructive functors have been introduced in [3], Definitions 2 and 10. Since, as it has been shown in [3], many functors relevant to Theory of Enumerations are constructive functors, this additional requirement seems