We analyze the stability of radiative shock waves of expanding (diverging) flows. Such flow structures develop when a fast wind from a central object expands against a denser and slower medium. The fast wind's material passes through a shock wave, and then cools and decelerates. We semianalytically study the stability of the fundamental and first overtone radial modes, for spherically symmetric flows, assuming power law cooling functions. We find that radiative shocks of diverging flows get more stable as the deviation from planarity increases. We apply the results to protoplanetary nebulae, and find that the overstability is likely to be effective during a period of ∼300 yr, when the central star wind's velocity increases from ∼150 to ∼300 km s-1. The instability can reveal itself via semiperiodic variation of some emissions lines, with semiperiods of fewX10 yr, and, if nonradial modes are overstable, in the development of clumps. Our results further stress the necessity of accurately incorporating the evolution with time of the wind and radiation from the central star when modeling planetary nebulae formation.