w-hyponormal operators generalize p-hyponormal operators but repeated Aluthge transformations of a w-hyponormal operator improve the hyponormality of the operator. Herein, we set out to investigate some of the conditions under which such transformations result into a normal operator. And eventually, we will extend our observations to check the normality of the products of any two such transformations.

normal, quasinormal, n-Power normal, w-hyponormal, Aluthge transforms.