The main purpose of this paper was to continue the study of separation axioms which is
introduced in part I (Kandil et al., 2015). Whereas the part I (Kandil et al., 2015) was devoted to the
axioms I PT i -ordered spaces, i = 0 , 1 , 2 , in the part II the axioms I PT i -ordered spaces, i = 3 , 4 , 5
and I PR j -ordered spaces, j = 2 , 3 , 4 are introduced and studied. Clearly, if I = { φ} in these axioms,
then the previous axioms (Singal and Singal, 1971; Abo Elhamayel Abo Elwafa, 2009) coincide with
the present axioms. Therefore, the current work is a generalization of the previous one. In addition,
the relationships between these axioms and the previous one axioms have been obtained. Some exam-
ples are given to illustrate the concepts. Moreover, some important results related to these separations
have been obtained