The linear and weakly nonlinear instability of a continuous model of the Heton cloud of Hogg and Stommel is studied. Particular attention is paid to the manner in which the continuous model presented here overlaps in behavior the point vortex dynamics described by Hogg and Stommel. The Heton cloud, which consists of a region of cyclonic vorticity overlying anticyclonic vorticity in the layer below (or vice versa), develops wavelike perturbations on the cloud boundary if the perturbation wavelength is long enough compared to the deformation radius. This is shown to be the case for both cloud bands and cylindrical Heton clouds. An analysis of the weakly nonlinear behavior of the Heton cloud band shows that the interaction of the fundamental wave with its next harmonic leads to nonlinear instability. The resulting explosive behavior is suggestive of the cloud fragmentation found in the point vortex model.