We reconsider the generation of convex hulls of fuzzy sets and establish the theory of recession cones for convex fuzzy sets. The classical theorem of Carathéodory is extended from ordinary convex analysis in Rⁿ to the fuzzy case. Two elementary applications of recession cones are presented: one on the characterization of boundedness of convex fuzzy sets, the other on the decomposition of unbounded convex fuzzy sets.