  We introduce the notion of Atiyah class of a generalized holomorphic vector
bundle, which captures the obstruction to the existence of generalized
holomorphic connections on the bundle. As in the classical holomorphic case,
this Atiyah class can be defined in three different ways: using \v{C}ech
cohomology, using the first-jet short exact sequence, or adopting the Lie pair
point of view.
