A theory of signatures for odd-dimensional links in rational homology spheres is studied via their generalized Seifert surfaces. The jump functions of signatures are shown invariant under appropriately generalized concordance and a special care is given to accommodate one-dimensional links with mutual linking. Furthermore our concordance theory of links in rational homology spheres remains highly nontrivial after factoring out the contribution from links in integral homology spheres. (C) 2002 Elsevier Science Ltd. All rights reserved.