In this paper we use a dynamic model to analyze the composition and stability of international environmental agreements (IEAs) in an asymmetrical framework. Signatory countries are assumed to optimize the total welfare of the international agreement's members, while non-signatory countries optimize their own individual welfare, taking into account the dynamics of the pollution stock. Our model is calibrated using data from the MERGE climate policy assessment model. We briefly review two contrasting approaches to define stability of IEAs, and provide a numerical illustration in each case.