Enumerating the isomorphism or equivalence classes of several types of graph coverings is one of the central research topics in enumerative topological graph theory.A covering projection p from a Cayley graph Cay(Γ,X) onto another Cayley graph Cay(Q,Y) is called typical if the function p:F → Q on the vertex sets is a group epimorphism.A typical covering is called abelian (or circulant,respectively) if its covering graph is a Cayley graph on an abelian (or a cyclic,respectively) group.Recently,the equivalence classes of connected abelian typical prime-fold coverings of a circulant graph are enumerated.As a continuation of this work,we enumerate the equivalence classes of connected abelian typical cube-free fold coverings of a circulant graph.