AbstractAk‐hypertournamentHonnvertices () is a pair, whereVis the vertex set ofHandAis a set ofk‐tuples of vertices, called arcs, such that for all subsetswith,Acontains exactly one permutation ofSas an arc. Recently, Li et al. showed that any strongk‐hypertournamentHonnvertices, where, is vertex‐pancyclic, an extension of Moon's theorem for tournaments. In this article, we examine several generalizations of regular tournaments and prove the following generalization of Alspach's theorem concerning arc‐pancyclicity: Every Σ‐regulark‐hypertournament onnvertices, where, is arc‐pancyclic.