\( M^{n}(c) \), \( c \in \mathrm{R} \) is a complete simply connected complex space form which is complex analytically isometric to three classical manifolds. The authors define a real hypersurface in \( M^{n}(c) \) and it turns out that there exists an almost contact metric structure on the real surface denoted by \((\Phi, \xi, \eta,g) \).The notion of real hypersurface of type \( (A) \) is given by Cecil-Ryan (2015) and Niebergall-Ryan (1997). The \( (1,1) \) tensor field \( L = \Phi A - A \Phi \), where \( A \) stands for the shape operator of the hypersurface is called the structure Lie operator of a real hypersurface. Then the Reeb recurrence condition for \( L \), i.e. (1) \( \nabla_{\xi} L = \omega(\xi) L \) for certain one form \( \omega(\xi) \) and the Lie Reeb recurrence condition (2) \( \mathcal{L}_{\xi} L = \omega(\xi) L \)for \( L \) are introduced. According to Theorem 1.4 (main result) on a real hypersurface in a non-flat complex form the hypersurface is of type \( (A) \iff L \) is Reeb recurrent operator (1) \( \iff L \) is Lie Reeb recurrent operator (2).