We will discuss the 'geodesic flow' on $SL(3,R)/\Gamma$ and invariant measures. Unlike the case of commuting toral automorphisms there are non-trivial ergodic measures possible. However, we will characterize the Haar measure using conditional measures and entropy. This is a joint work with Anatole Katok, and part of the more general problem to understand the invariant measures for higher rank abelian actions -- as in Furstenberg's problem.