The storage capacity of the fuzzy bidirectional associative memories (FBAMs) is studied in this paper. The necessary and sufficient conditions in theory are established for the associations to be reliably stored and recalled in an FBAM. Based on them, the probability for associations to be reliably stored and recalled in an FBAM is studied. For the binary FBAMs, particularly, those constructed by the max-min learning rule, the representation of attractors is presented, and the formula for calculating the number of attractors is obtained.