Abstract: We consider a diffusive Rosenzweig - MacArthur predator-prey model in the situation when the prey diffuses at the rate much smaller than that of the predator. Depending on the parameter regime, phenomenologically different types of fronts exist in this model. In particular, there exists a regime when the underlying dynamical system in a singular limit is reduced to a scalar Fisher-KPP equation and, according to the Geometric Singular Perturbation Theory, the fronts supported by the full system are small perturbations of the Fisher-KPP fronts. It is of interest whether the stability of the fronts is also governed by the scalar Fisher-KPP equation. The techniques of the analysis include a construction of unstable augmented bundles and their treatment as multiscale topological structures. This is a joint project with Stephane Lafortune, Yuri Latushkin, and Vahagn Manukian.