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In this paper, we study the Cauchy problem for the modified Camassa-Holm equation mt + umx + 2ux m = 0, m =(1- δ2x)2u,u(x, 0) = u0(x) ∈ Hs(R), x ∈ R, t > 0,and show that the solution map is not uniformly continuous in Sobolev spaces Hs(R) for s > 7/