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To give an almost quaternionic structure on a 4n-manifold $M$ is equivalentto give its bundle of twistors $Z(Q)\longrightarrow M$. When $Q$ is invariantunder a torsion free connection, $Z(Q) $ can be provided with an almost complexstructure $ \mathbb J $. In the case $ n = 1 $ Atiyah, Hitchin and Singer haverelated the integrability of $ \mathbb J $ to the geometry of $ (M, Q) $. For $n> 1 $ Salamon showed that the almost complex structure $ \mathbb J $ on $ Z(Q) $ is always integrable. The purpose of this article is to extend theseresults to the generalized complex geometry. We begin by defining the conceptof almost generalized quaternionic manifolds $ (M, g, \mathcal Q ) $. We willsee that we can associate a twistor space denoted by $ \mathcal Z( \mathcal Q)$ which is a $ \mathbb S^2$-bundle over $ M $. When $\mathcal Q$ is invariantunder a generalized torsion free connection, then $ \mathcal Z(\mathcal Q) $comes with an almost generalized complex structure $\mathbb J$. Whatever thedimension of $ M $ is, we give a criterion for integrability of the almostgeneralized complex structure $ \mathbb J $ on $ \mathcal Z(\mathcal Q) $. Inthe particular case where $ (M, g,\mathcal Q) $ is a generalized quaternionicK\"ahler manifold, we show that $\mathbb J$ is always integrable as soon as$n>1$. We illustrate this work by giving several examples of generalizedquaternionic K\"ahler manifolds for which the almost generalized complexstructure $ \mathbb J $ on the twistor space $ \mathcal Z(\mathcal Q) $ isintegrable.

Espace des twisteurs d'une vari\'et\'e quaternionique K\"ahler g\'en\'eralis\'ee