The propagation characteristics of waves upstream and downstream of quasi-parallel shocks are investigated by using two-dimensional hybrid simulations. At low Alfv¿n Mach numbers MA≲2, the shock is initially associated with upstream phase-standing whistlers. At later times, backstreaming ions excite longer-wavelength whistlers via the right-hand resonant ion/ion instability. As anticipated from linear theory, these waves are found to propagate along the magnetic field. Their group velocity is larger than or comparable to the upstream flow speed, and as a result, the waves remain in the upstream region. At higher MA>3 these waves are convected back into the shock, causing its re-formation and downstream perturbations. Shock transmitted waves mode-convert into Alfv¿n/ion-cyclotron waves which have a wavevector along the shock normal (pointing upstream) and convect downstream. The two-dimensional simulation results confirm our earlier suggestion that the upstream waves should be field aligned, and that their convection into the downstream is associated with linear mode conversion into the Alfv¿n/ion-cyclotron branch. ¿ American Geophysical Union 1993