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This paper examines the stability of a thin, spherical shock against dynamic and gravitational perturbations when the wavelength of the perturbation is large compared to the thickness of the dense shell. For dynamic perturbations, it is found that a spherical isothermal shock, driven by a hot gas, is overstable against small perturbations. As a result, the fragmentation of the shell proceeds in an oscillatory manner. The smaller wavelength perturbations are most unstable, with the maximum growth rate being comparable to the inverse of the time it takes sound waves to propagate through the shell thickness. The nonradiating case is not subject to this overstability unless d ln P/d ln rho is close to 1. The overstability can appear in cases where there is an ambient magnetic field. The growth of gravitationally driven perturbations is also considered.