A fuzzy subset of a fuzzy topological space is fuzzy sequentially compact if any sequence of fuzzy points in has a generalized fuzzy subsequence which is fuzzy convergent in . More generally we say that a fuzzy subset of a fuzzy topological space is -fuzzy sequentially compact if any sequence of fuzzy points in has a generalized fuzzy subsequence such that where is a function from a suitable subset of the set of all sequences of fuzzy points in . We investigate some of the basic properties of this compactness and suggest some open problems.