Abstract
In this paper, we have defined ordered quasi-G-ideals and ordered bi-Gamma-ideals in ordered Gamma-semirings by defining the relation "<=" in ordered Gamma semiring S as a <= b if a + x = b for any a, b, x epsilon S. By using this relation we have shown that ordered quasi-Gamma-ideals and ordered bi-Gamma-ideals in ordered Gamma-semirings are generalization of quasi-ideals and bi-ideals in ordered semirings. Properties of many types of ordered Gamma-ideals including (semi)prime, (strongly) irreducible, and maximal ordered quasi-Gamma-ideals and ordered bi-Gamma-ideals in ordered Gamma-semirings S have been studied.