The paper is devoted to the introduction and study of the concepts of certain classes of functions between fuzzy topological spaces. Each of these functions presents a stronger form of the fuzzy continuous functions. These maps have been characterized and investigated mainly in the light of the notions of q-neighbourhoods, quasi-coincidence, fuzzy δ-closure and ds-neighbourhoods. They have also been compared as to their mutual dependence as also with regard to their interactions with certain other fuzzy non-continuous functions. © 1990.