  We obtain a partial parallelism of the complex structure on K\"ahler Finsler
manifolds. As applications, we prove Synge-Tsukamoto theorem and Bonnet-Myers
theorem for positively curved K\"ahler Finsler manifolds. Moreover, we
generalize a comparison theorem due to Ni-Zheng by introducing the notion of
orthogonal Ricci curvature to K\"ahler Finsler geometry.
