This paper is about conformal complex Finsler metrics of constant holomorphic curvature. We deal with generalized Einstein conformal complex Finsler metrics. The study is realized with respect to Chern complex linearconnection on the pull-back tangent bundle π*(T' M) . The final section applies our results to some examples, better illustrating the interest for this work.

Key Words: complex Finsler space, constant holomorphic curvature, conformal complex Finsler metric.

2000 Mathematics Subject Classification: Primary: 53B40, Secondary: 53C60.