AbstractLet D be a hamiltonian digraph. A nonempty vertex set X⊆V(D) is called an H-force set of D if every X-cycle of D (i.e. a cycle of D containing all vertices of X) is hamiltonian. The H-force number h(D) of a digraph D is defined to be the smallest cardinality of an H-force set of D. In this paper, the minimal H-force sets of locally semicomplete digraphs are characterized and the H-force number is given.