Spacetimes formed from the cartesian product of Minkowski space and a compact Ricci flat space with special holonomy play an important role in supergravity and string theory. In this talk I will discuss two results concerning the global, nonlinear stability of such spacetimes: one is work in collaboration with Andersson, Blue and Yau, the other is upcoming work with Huneau and Stingo. Both results are related to claims of Penrose and Witten concerning the validity of supergravity and string theory.