A (d−1)-dimensional simplicial complex is called balanced, if its 1-skeleton is d-colorable. In this talk, I will discuss upper bounds for the graded Betti numbers of the Stanley-Reisner rings of this class of simplicial complexes. Our results include both, bounds for the Cohen-Macaulay case and for the general situation. Previously, upper bounds have been shown by Migliore and Nagel, and Murai for simplicial polytopes, Cohen-Macaulay complexes and normal pseudomanifolds. If time permits, I will also mention, what can be said for balanced normal pseudomanifolds. This is joint work with Lorenzo Venturello.