This paper is about the holomorphic flag curvature of complex Finsler
metrics. For a complex Finsler space

, the holomorphic flag curvature
with respect to the Chern complex linear connection on the pull-back tangent
bundle is defined. By means of holomorphic curvature, a special approach is
devoted to obtain characterization of the holomorphic flag curvature

Finally we deal with holomorphic flag curvature of the generalized Einstein
complex Finsler spaces.