The purpose of this paper is to study the erosion of eddies by filamentation in a shallow-water model where both fast and slow components of the dynamics coexist. In presence of inertia-gravity waves this filamentation process is indeed found to be altered. However, the information required to analyze the filamentation process is shown to be entirely captured by the slow component of the flow and regions of filament ejection can be identified from a diagnostic criterion based on instantaneous slow quantities. This is illustrated numerically in a reduced gravity model for an initial elliptic vortex of distributed potential vorticity in presence of Poincare waves. (C) 2004 American Institute of Physics.