  This article studies descent theory in the setting of Berkovich spaces. We
give sufficient conditions for a given fibered category over the category of
k-affinoid algebras to be a stack for the Berkovich analogue of the
faithfully-flat topology. We give some applications to the faithfully flat
descent of morphisms and show that some descent data are always effective. We
also show that the property of being algebraic for a morphism between the
analytification of two schemes is a local property for the faithfully-flat
topology.
