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The main goal of this paper is to generalize some Li-Yau type gradientestimates to Finsler geometry in order to derive Harnack type inequalities.Moreover, we obtain, under some curvature assumption, a general gradientestimate for positive solutions of the heat equation when the manifold evolvingalong the Finsler Ricci flow.

Harnack inequalities for positive solutions of the heat equation on closed Finsler manifolds