In this paper the coupling of a parabolic model with a system of local kinetic equations is analyzed. A space–time separated representation is proposed for the global model (this is simply the radial approximation proposed by Pierre Ladeveze in the LATIN framework (Non-linear Computational Structural Mechanics. Springer: New York, 1999)). The originality of the present work concerns the treatment of the local problem, that is first globalized (in space and time) and then fully globalized by introducing a new coordinate related to the different species involved in the kinetic model. Thanks to the non-incremental nature of both discrete descriptions (the local and the global one) the coupling is quite simple and no special difficulties are encountered by using heterogeneous time integrations. Copyright © 2009 John Wiley & Sons, Ltd.