  We study the Pimsner algebra associated with the module of continuous
sections of a Hilbert bundle, and prove that it is a continuous bundle of Cuntz
algebras. We discuss the role of such Pimsner algebras w.r.t. the notion of
inner endomorphism. Furthermore, we study bundles of Cuntz algebras carrying a
global circle action, and assign to them a class in the representable KK-group
of the zero-grade bundle. We compute such class for the Pimsner algebra of a
vector bundle.
