Ulysses observations show that many coronal mass ejections observed at high heliographic latitudes expand because they initially have higher internal pressures than that of the surrounding solar wind. This expansion commonly drives a shock wave into the ambient wind in all directions. In the analogous process of an explosion in the Earth's atmosphere, the expansion is followed by an implosion at the center of the disturbance. Ulysses observations to date, however, suggest that these over-expanding CMEs do not implode, at least within 5.4 AU, in spite of the fact that many have central pressures at large heliocentric distances that are considerably lower than that of the surrounding solar wind. We use fluid simulations to investigate whether these CMEs might eventually collapse at larger heliocentric distances. We find that for a wide range of initial perturbations close to the Sun the CMEs do not implode at any heliocentric distance. Implosion does not occur because of the overall reduction in pressure associated with the spherical expansion of the solar wind. ¿ 1998 American Geophysical Union