We say that the operators A;B on Hilbert space satisfy the Fuglede-Putnam theorem if AX = XB for some X implies A*X = XB*. We show that if A is k quasihyponormal and B* is an injective p-hyponormal operator, then A, B satisfy the Fuglede-Putnam theorem. As a consequence of this result, we obtain the range of the generalized derivation induced by the above classes of operators is orthogonal to its kernel.