Introduction. Let X be a compact metric space, and 21 be the collection of all nonempty closed subsets of X. The mth homotopy group Mllm(2x, A) for set-valued functions has been studied in [3]. By applying the results of [1], we will prove that if W(n) is the set of all cellular subsets of Sn and pCSn, then MTIm(W(n), p) is isomorphic to the ordinary mth homotopy group of S". Let Im be the product of m closed unit intervals, and Bd Im be the boundary of Im. Each point xCIm is represented by x = (xi, * * *, xm), 0