  A detailed numerical stability analysis of the static, spherically symmetric
globally regular solutions of the Einstein-Yang-Mills equations with a positive
cosmological constant, Lambda, is carried out. It is found that the number of
unstable modes in the even parity sector is n for solutions with n=1,2 nodes as
Lambda varies. The solution with n=3 nodes exhibits a rather surprising
behaviour in that the number of its unstable modes jumps from 3 to 1 as Lambda
crosses (from below) a critical value. In particular the topologically 3-sphere
type solution with n=3 nodes has only a single unstable mode.
