The so-called p-local comapct groups are algebraic models for (p-completed) classifying spaces of finite groups, compact Lie groups, and p-compact groups, among other examples. In this talk I will present a p-local version of a result of Friedlander and Mislin which relates classifying spaces of compact Lie groups with telescopes of classifying spaces of finite groups. This result allows to deduce a p-local versions of the Stable Elements Theorem of Cartan and Eilenberg to compute the mod p cohomology of a classifying space. If time allows, I will comment on other consequences of the approximation theorem.