A hypergroup, in the sense of Marty (1934), is a set H equipped with an associative hyperoperation \(\cdot: H\times H\to P(H)\) which satisfies the property that \(xH=Hx=H\), for all \(x\in H\). We consider hypergroups constructed from ordinary semigroups which generalizes the notion of P- hypergroups introduced by the author [Acta Univ. Carol., Math. Phys. 22, No.1, 3-6 (1981; Zbl 0495.20042)]. In particular we study the cyclicity and reversibility properties of these structures.