  In this paper we show the classical global stability of the flat Kaluza-Klein
spacetime, which corresponds to Minkowski spacetime in $\m R^{1+4}$ with one
direction compactified on a circle. We consider small perturbations which are
allowed to vary in all directions including the compact direction. These
perturbations lead to the creation of massless modes and Klein-Gordon modes. On
the analytic side, this leads to a PDE system coupling wave equations to an
infinite sequence of Klein-Gordon equations with different masses. The
techniques we use are based purely in physical space using the vectorfield
method.
