Unary iterative hyperidentities (u.i.h.) are conditions of the form \(F^a(x)=F^{a+b}(x)\), where \(F\) is a unary operation symbol, and \(a,b\geq 1\). Let \(V_{n,m}\) denote the variety of [inverse] semigroups defined by the identity \(x^n=x^{n+m}\). For each u.i.h., the largest variety of [inverse] semigroups satisfying it is found; the variety is one of \(V_{n,m}\), except for one special case for inverse semigroups. For each variety of [inverse] semigroups \(V_{n,m}\), the minimal (i.e. the strongest) u.i.h. holding in it is found.