Dedicated to the memory of Professor CHENG MinDe on the occasion of the centenary of his birth

In this paper, we derive W 1,∞ and piecewise C1,α estimates for solutions, and their t-derivatives, of divergence form parabolic systems with coefficients piecewise Hölder continuous in space variables x and smooth in t. This is an extension to parabolic systems of results of Li and Nirenberg [Comm Pure Appl Math, 2003, 56: 892–925] on elliptic systems. These estimates depend on the shape and the size of the surfaces of discontinuity of the coefficients, but are independent of the distance between these surfaces.