Given a C2 semi-algebraic mapping F : R N → Rp , we consider its restriction to W ,→ R N an embedded closed semi-algebraic manifold of dimension n − 1 ≥ p ≥ 2 and introduce sufficient conditions for the existence of a fibration structure (generalized open book structure) induced by the projection FkF k : W \F −1 (0) → S p−1.