Abstract: It is an important method to construct and study semigroups by the semidirect product and wreath product of two semigroups.At present,there are many reports in the semidirect product and wreath product of semigroups(without ordered relation),but there are few references in the semidirect product and wreath product of ordered semigroups.I-regular and I-inverse semigroups are two important classes ordered semigroups as a generalization of regular and inverse semigroups.In this paper,the semidirect product of two pomonoids are introduced,and necessary and sufficient condition are determined for the semidirect product of two ordered monoids to be I-regular and I-inverse semigroup,as an application in wreath product,main theorems in reference \ and \ are obtained.