Electromagnetic simulations are used to investigate the nonlinear evolution of ULF (magnetosonic) waves. These waves have been observed upstream of planetary bow shocks and at Comet Giacobini-Zinner. The simulations show that these waves steepen to form subcritical dispersive shock waves. The steepening process is due to the generation of a broad spectrum of waves on the magnetosonic-whistler branch. As a result, the waveform spreads in space and the original elliptical polarization of the wave changes to linear. Also, the fastest propagating waves overtake the steepened front and form a circularly polarized precursor. Interpretation of the steepened waves as shocks suggest that Comet Giacobini-Zinner did not have a single bow shock but instead a transition region consisting of a series of shocks which were convected by the solar wind. ¿ American Geophysical Union 1988