Abstract. We prove that if G is a 2-connected non-complete graph on n vertices, then Sz(G)-W(G)>=2n-6. Furthermore, the equality is attained if and only if G is the complete graph on n-1 vertices Kn-1 with an extra vertex attached to either 2 or n-2 vertices of Kn-1. Using our method we strengthten some previous results on the difference between the Szeged and Wiener indices.