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Nearly K\"{a}hler and K\"{a}hler-Codazzi type manifolds are defined in a verysimilar way. We prove that nearly K\"{a}hler type manifolds have sense just inHermitian and para-Hermitian contexts, and that K\"{a}hler-Codazzi typemanifolds reduce to K\"{a}hler type manifolds in all the four Hermitian,para-Hermitian, Norden and product Riemannian geometries.

On nearly K\"{a}hler and K\"{a}hler-Codazzi type manifolds