  We show how the classical Moser Lemma from symplectic geometry extends to
generalized complex structures (GCS) on arbitrary Courant algebroids. For this,
we extend the notion of Lie derivative to sections of the tensor bundle
$(\otimes^i E)\otimes(\otimes^j E^*)$ with respect to sections of the Courant
algebroid $E$ using the Dorfman bracket. We then give a cohomological
interpretation of the existence of one-parameter families of GCS on $E$ and of
flows of automorphims of $E$ identifying all GCS of such a family. In the
particular cases of symplectic, we recover the results of Moser. Finally, we
give a criterion to detect the local triviality of arbitrary GCS which
generalizes the Darboux-Weinstein theorem.
