The authors consider four kinds of parameter free dual models for the following fractional complex programming problem involving nonlinear analytic functions with generalized convexity: \[ \text{Minimize} \frac{\text{Re} [f(z, \overline z)+(z^HAz)^{1/2}]} {\text{Re}[g(z,\overline z)-(z^HBz)^{1/2}]}= \frac {\psi(z)}{\varphi(z)}\tag{P} \] \[ \text{subject to }z\in\mathbb{C}^n\text{ and }h(z, \overline z)\in S \subset\mathbb{C}^m \] where \(f,g:\mathbb{C}^{2n}\to\mathbb{C}\) and \(h: \mathbb{C}^{2n} \to\mathbb{C}^m\) are analytic functions on a specific set \(Q=\{(z,z')\in \mathbb{C}^n \times \mathbb{C}^n\mid z'=\overline z\}\subset \mathbb{C}^{2n}\); \(z^H\) means the transpose of \(\overline z\); \(S\) is a polyhedral cone; \(A\) and \(B\) are positive semidefinite Hermitian matrices. It is assumed that \(\psi(z)\geq 0\) and \(\varphi (z)>0\). The weak, strong and strict converse duality theorems are proved.