A poe-groupoid is a po-groupoid endowed with a greatest element e. The same for poe (le)-semigroups. In this short note, the author continues his study of regularity of poe-semigroups. The following result is proved: Theorem. Let S be a poe-semigroup. If S is regular, then the right (left) ideal elements of S are idempotent and for every right ideal element x and every left ideal element y of S such that \((x\wedge y)e\wedge e(x\wedge y)\) exists, the product xy is a quasi-ideal element of S. As a consequence of the above, the following characterization of the le-semigroups which are regular is given: If S is an le-semigroup, then S is regular iff the following condition holds: For every right ideal element x and every left ideal element y we have \(x^ 2=x\), \(y^ 2=y\) and xy is a quasi-ideal element. For further reference see [Semigroup Forum 19, 111-121 (1980; Zbl 0434.06015), and ibid. 25, 213- 222 (1982; Zbl 0499.06012)], both by the same author.