Rhythmic interlimb coordination is characterized by attraction to stable phase and frequency relations. Sudden transitions between the resulting coordination patterns, which are observed when movement frequency is gradually increased, have been modeled at two formally related levels: a potential function and a system of coupled oscillators. At the latter level of the model, two alternative derivations resulted in different predictions with respect to the way in which movement frequency and amplitude affect pattern stability. Our recent results contradicted the prevailing version of the model, which predicts that the influence of movement frequency is fully mediated by the associated changes in amplitude. Although the results could be reconciled with the alternative derivation of the model in which time delays (possibly related to neurophysiological delays) were incorporated, the absence of amplitude-mediated effects on pattern stability challenges both versions of the model. It is argued that by studying coordination dynamics at the level of the potential function as well as at the level of coupled oscillators, new insights into the way in which control parameters influence pattern dynamics may be obtained. This may open up ways to link the coordination dynamics to specific characteristics of the movements of the limbs and the way in which they interact.PsycINFO classification: 2300; 2330.