Double Frobenius algebras (or dF-algebras) were recently introduced by the author. The concept includes finite-dimensional Hopf algebras, adjacency algebras of (non-commutative) association schemes, andC-algebras (character algebras). In this paper we define certain kinds of morphisms of dF-algebras and develop their basic theory. The morphisms generalize homomorphisms of Hopf algebras and ofC-algebras.