The manifolds referred to in the title of the paper under review are smooth manifolds modeled on Fréchet spaces, for which the values of the coordinate changes are linear operators that satisfy the Lipschitz condition with respect to some complete invariant metrics that define the topology of the model Fréchet spaces. It is well known that the study of locally convex manifolds is more difficult than the study of Banach manifolds, due to the failure of some basic results like the inverse function theorem or local inversion theorem. Nevertheless, one shows in the present paper that in the case of bounded Fréchet manifolds the bounded Fréchet tangent bundle has the structure of a vector bundle, and one also obtains interesting results on the second tangent bundle in the presence of a linear connection.