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This paper is devoted to the study of some new classes of operators on Hilbert space called (n,m) -power D -normal ( [(n,m)DN] ) and (n,m) -power D -quasi-normal ( [(n,m)DQN] ) , associated with a Drazin invertible operator using its Drazin inverse. Some properties of [(n,m)DN] and [(n,m)DQN] are investigated and some examples are also given. Mathematics subject classification (2010): 47B15, 47B20, 47A15.

On the classes of (n,m)-power D-normal and (n,m)-power D-quasi-normal operators