  We consider manifolds endowed with a contact pair structure. To such a
structure are naturally associated two almost complex structures. If they are
both integrable, we call the structure a normal contact pair. We generalize the
Morimoto's Theorem on product of almost contact manifolds to flat bundles. We
construct some examples on Boothby--Wang fibrations over contact-symplectic
manifolds. In particular, these results give new methods to construct complex
manifolds.
