The following problem was raised by K. Borsuk in [4]. "Let S denote the k-dimensional sphere. Does there exist a compactum X which is S-movable for k=l, 2,...n, but is not n-movable?" In this paper, we will construct such a continuum X for the case of n>__2.The concepts of n-movability and A-movability were originally given by K. Borsuk in [3] and [4], and they are equivalent to the following definitions. Let X be a compactum and X--{X, p,,N} be an ANR-sequence associated with X, where each X, n e N, is a regular ANR-space (see [6]).Definition 1 (Y. Kodama and T. Watanabe [6]). A compactum X is said to be k-movable if for each n e N there is n'e N, n'>=n, such that for each n"e N, n">_n, and for each compact set KX, with dim K<=k, there is a map f,, "KoX,, 'satisfying the homotopy relation" P,,f,,'Pn" " KX. Definition 2. Let A be a compactum. A compactum X is said to be A-movable if for each n e N there is n' e N, n'>=n, such that for each n" e N, n":>n, and for each map f AX,, there is a map f ,, AoX,, satisfying the homotopy relation" p,,f,,p,f" A---X.The equivalence of the concept of A-movability in Definition 2 and the original one can be shown by the same way as in the proof of Theorem 3 of [5].Our example is homeomorphic to the continuum constructed by K. Borsuk [2]. For completeness we give its construction. Consider the following compact subsets of an Euclidean 3-space R 3" A1-----{(x, y, z) x2+ y2+ z2=5, Ixl___2, U {(x, y, z) x2+ y2= 1, B0-----{(x, y, z) lx2+ y2+ z2__ 5, ]xl y, z) x + y + z=5, x>__2} A={(x,y,z)l(x--4n+4, y,z) eA}, n=2, 3, B={(x, y, z) (x--4n +4, y, z) e B},