We investigate the generalized derivations and show that every generalized derivation on a simple Hilbert C ∗ -module is either closable or has a dense range. We also describe dynamical systems on a full Hilbert C ∗ -module M over a C ∗ -algebra A as a one-parameter group of unitaries on M and prove that if α : R → U (M) is a dynamical system, where U (M) denotes the set of all unitary operator on M, then we can correspond a C ∗ -dynamical system α 0 on A such that if δ and d are the infinitesimal generators of α and α 0 respectively, then δ is a d-derivation.

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