This article deals with generalized differentiable fuzzy functions. Specifically, we give some characterizations of generalized Hukuhara differentiable fuzzy functions through the differentiability of their endpoint functions. Then, we introduce a differentiability concept that is more general than the generalized Hukuhara differentiability and extend the above characterization to this new type of differentiability as well as to g-differentiable fuzzy functions. These characterizations are useful tools for the calculus of derivatives of fuzzy functions. (C) 2015 Elsevier B.V. All rights reserved.