  We consider the nonlinear stability of the Kaluza-Klein monopole viewed as
the static solution of the five dimensional vacuum Einstein equations. Using
both numerical and analytical methods we give evidence that the Kaluza-Klein
monopole is asymptotically stable within the cohomogeneity-two biaxial Bianchi
IX ansatz recently introduced in \cite{bcs}. We also show that for sufficiently
large perturbations the Kaluza-Klein monopole loses stability and collapses to
a Kaluza-Klein black hole. The relevance of our results for the stability of
BPS states in M/String theory is briefly discussed.
