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We prove C1,α almost everywhere regularity for weak solutions in the space W1,k(ΩΩ, RN) of the systems -DαAia(x, u, Du) = Bi(x, u, Du) under the weak / A(x0, u,p + Dφ). Dφdy _> λ/(|DФ|2 + |DФ|k)dy.