In this paper we analyze the existence and uniqueness of solutions for a fuzzy initial value problem of kind x'(t) = f(t,x(t)), x(t0) = x0, where f: T x X --> X is a fuzzy-valued mapping, T is a time interval, X is a class of fuzzy sets, x0 ∈ X and to ∈ T. We consider x'(t) as a generalization of the Hukuhara derivative.