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We introduce the notion of ordered quasi--ideals of regular ordered -semigroups and study the basic properties of ordered quasi--ideals of ordered -semigroups. We also characterize regular ordered -semigroups in terms of their ordered quasi--ideals, ordered right -ideals, and left -ideals. Finally, we have shown that (i) a partially ordered -semigroup is regular if and only if for every ordered bi--ideal , every ordered -ideal , and every ordered quasi--ideal , we have and (ii) a partially ordered -semigroup is regular if and only if for every ordered quasi--ideal , every ordered left -ideal , and every ordered right--ideal , we have that .

On Ordered Quasi-Gamma-Ideals of Regular Ordered Gamma-Semigroups