  The conformal properties of complex Finsler metrics are studied. We give a
characterization of a compact complex Finsler manifold to be globally conformal
K\"ahler. The critical points of the total holomorphic curvature and total
Ricci curvature in the volume preserved conformal classes are studied. The
stability of critical K\"ahler Finsler metrics is obtained. A Yamabe type
problem for mean Ricci curvature is considered.
