  In this paper, we find that the integrated form $d_F$ of a complex Finsler
metric $F$ is inner. The distance $d_F$ is complete if and only if every closed
bounded subset of a complex manifold $M$ is compact. We prove a version of
theorem for normal families of holomorphic mappings between two complex Finsler
manifolds, i.e, the theorem of Montel in complex Finsler manifolds. Our results
extend the basic theorem of strongly negatively curved families for a Hermitian
manifold [Wu, Acta Math. 119(1967), 193-233] or [Grauert, Reckziegel, Math. Z.
89(1965), 108-125]. As applications, we obtain a complex Finsler version of
theorems $A$-$F$ in [Wu, Acta Math. 119(1967), 193-233], including the
Cartan-Carath\'eodory-Kaup-Wu theorem, the theorem of the automorphism group on
a complex Finsler manifold and some rigid results.
