Summary: Considering the question under what conditions an ordered semigroup (or semigroup) contains at most one maximal ideal we prove that in an ordered groupoid \(S\) without zero there is at most one minimal ideal which is the intersection of all ideals of \(S\). In an ordered semigroup for which there exists an element \(a \in S\) such that the ideal of \(S\) generated by \(a\) is \(S\), there is at most one maximal ideal that is the union of all proper ideals of \(S\). In ordered semigroups containing a unit, there is at most one maximal ideal that is the union of all proper ideals of \(S\).