The Kaluza-Klein theories represent the classical mathematical approach to the unification of general relativity with electromagnetism and more generally with gauge fields. In these theories, general relativity is considered in 1+3+d dimensions and in the simplest case d=1 dimensional gravity is compactified on a circle to obtain at low energies a (3+1)-dimensional Einstein-Maxwell-Scalar systems.  In this talk I will discuss the problem of the classical global stability of Kaluza-Klein theories when d=1. This is a joint work with C. Huneau and Z. Wyatt.