 We study the influence of the particular form of the functional response in twodimensional predatorprey models with respect to the stability of the nontrivial equilibrium. This equilibrium is stable between its appearance at a transcritical bifurcation and its destabilization at a Hopf bifurcation giving rise to periodic behavior. Based on local bifurcation analysis we introduce a classification of stabilizing effects. The classical RosenzweigMacArthur model can be classified as weakly stabilizing, undergoing the paradox of enrichment, while the wellknown BeddingtonDeAngelis model can be classified as strongly stabilizing. Under certain conditions we obtain a complete stabilization resulting in an avoidance of limit cycles. Both models, in their conventional formulation, are compared to a generalized, steadystate independent twodimensional version of these models, based on a previously developed normalization method. We show explicitly how conventional and generalized models are related and how to interpret the results from the rather abstract stability analysis of generalized models.
