  In this paper we introduce in study the projectively related complex Finsler
metrics. We prove the complex versions of the Rapcs\'{a}k's theorem and
characterize the weakly K\"{a}hler and generalized Berwald projectively related
complex Finsler metrics. The complex version of Hilbert's Fourth Problem is
also pointed out. As an application, the projectiveness of a complex Randers
metric is described.
