We examine the consequences of long-range effects on tumour cell migration. Our starting point are previous results of ours where we have shown that the migration patterns of glioma cells are best interpreted if one assumes attractive interactions between cells. Here we complement the cellular automaton model previously introduced by the assumption of the existence of a chemorepellent produced by the main bulk of large spheroids (in the hypoxic/necrotic areas). Visible effects due to the presence of such a substance can (...) be found in the density profiles of cells migrating out of a single spheroid as well as in the angular distribution of cells coming from two close-lying spheroids. These effects depend crucially on the diffusion speed of the chemorepellent. A comparison of the simulation results to experimental data of Werbowetski et al. allows to draw (tentative) conclusions on the existence of a chemorepellent and its properties. (shrink)