Martin Kassabov Cornell University We introduce and study the class of groups graded by root systems. We prove that if Φ is an irreducible classical root system of rank ≥2 and G is a group graded by Φ, then under certain natural conditions on the grading, the union of the root subgroups is a Kazhdan subset of G. As the main application of this theorem we prove that for any reduced irreducible classical root system Φ of rank ≥2 and a finitely generated commutative ring R with 1, the Steinberg group StΦ(R) and the elementary Chevalley group EΦ(R) have property (T) .