In this paper, we prove that for every p-hyponormal operator A, there corresponds a hyponormal operator A such that A and A have the same closed range points and same essential spectrum and same spectrum. This is then used to derive that if A is a p - hyponormal operator, B is any bounded linear operator and there exists a dense range operator X such that XB = AX, then (A) (B). We also prove that if A is a p-hyponormal operator and R(A) is closed or KerA = KerA , B is any bounded linear operator, B and A are quasisimilar, then (A) (B).