Summary: We introduce classes of graphs with bounded expansion as a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) $of G$ with rank $r, \nabla_r(G)$. For these classes we prove the existence of several partition results such as the existence of low tree-width and low tree-depth colorings. This generalizes and simplifies several earlier results (obtained for minor closed classes).