In this work we address the development of a timestepper based computational approach to analyse the dynamics of the Smoluchowski equation directly, bypassing the necessity of finding closures to construct low-order macroscopic models, while at the same time factoring out in a dynamic way the underlying continuous symmetry. This can be thought as a two-tier model reduction methodology for systems with continuous symmetries: going from models with a large numbers of degrees of freedom to more compact models, in terms of a smaller number of dependent variables, while also taking care of the underlying invariance. (C) 2006 Elsevier B.V. All rights reserved.