We analyze data of the AMPTE/IRM spacecraft downstream of a supercritical, quasi-perpendicular bow shock with an upstream &bgr; (ratio of thermal to magnetic pressure) greater than unity. The observed ion temperature anisotropy (Tp⊥>Tp∥) satisfies the mirror instability criterion, and the mirror growth rate is positive. We investigate the low-frequency magnetic fluctuations and find that several minutes downstream of the shock ramp the compressive mode dominates in two frequency intervals below the local proton gyrofrequency. Band-pass filtering of the two frequency ranges shows that the particle pressure and magnetic pressure vary in antiphase, as is typical for the mirror mode. In addition, we estimate the proton compressibility, that is, the ratio of the relative fluctuations of proton density and magnetic field, and the Alfv¿n ratio, that is, the ratio of fluctuations of the bulk velocity and the Alfv¿n velocity. Combining these results, we find strong indications for the existence of mirror waves in the region downstream of the bow shock. The observed spectrum of the mirror waves has a two-banded structure. ¿ 1998 American Geophysical Union