abstract: Two elements x,y in a Lie group G are said to be almost commutative if /x/,/y/ is in the center of G. The space of almost commuting elements is a good way to approach the space of commuting elements in G, a space of current interest. In this talk I will explain how the space of almost commuting elements in a compact Lie group splits after one suspension. This is a joint work with Alejandro Adem and Fred Cohen.