We study SYZ mirror symmetry in the context of non-Kaehler Calabi-Yau manifolds. In particular, we study the six-dimensional Type II supersymmetric $SU(3)$ systems with Ramond-Ramond fluxes, and generalize them to higher dimensions. We show that Four
ier-Mukai transform provides the mirror map between these Type IIA and Type IIB supersymmetric systems in the semi-flat setting. This is concretely exhibited by nilmanifolds.
