An asymptotic theory based on multipole expansions is presented for multiparticle interactions in unbounded, weakly viscoelastic, creeping flows. The theory accounts for non-Newtonian sphere-sphere interactions that are of order O(De(a/R)(2)), where De is the Deborah number, a the sphere radius and R is the sphere-sphere separation. Analytic expressions are derived for the non-Newtonian correction to the multisphere mobility matrix for non-neutrally buoyant sedimenting spheres, and for neutrally buoyant spheres suspended in a shear flow. It is shown that these expressions give rise to particle chaining in simulations of interacting spherical particles. (c) 2007 Elsevier B.V. All rights reserved.