The goal of this talk is to give a definition of two geometrical structures on a smooth manifold: a Nijenhuis operator and an F-structure. It is known that an F-structure on a manifold induces a (1,1)-tensor field that has a vanishing Nijenhuis torsion. A natural question is to find sufficient conditions for a Nijenhuis manifold to be an F-manifold. An answer to this question will be presented for a class of gl-regular Nijenhuis operator fields.