In this note we introduce the concept of completely prime and completely semiprime ideals for Γ-rings and study some of the properties of these ideals. Furthermore we introduce the concept of the completely prime radical of an ideal of a Γ-ring and also show that the upper radical determined by a class of completely prime rings is a special radical. We define an mc-system to give an elementwise characterization of the completely prime radical. Finally we show that if R is the right operator ring of a Γ ring H and W has a strong right unity, then there is a one-to-one correspondence between the completely prime ideals of R and that of M.