Potassium densities and temperatures were measured on board the German Research Vessel 'Polarstern' with the containerized IAP (Institute of Atmospheric Physics) K-lidar. Considerable wave activity was observed in the K density profiles as well as the temperature profiles, in particular during the night of May 23/24, 1996 over the South Atlantic ocean. A strong monochromatic wave was observed between 85 and 100 km. The calculated relative K density variations are in phase with the temperature variations at the bottom of the K layer and 180¿ out of phase at the top of the K layer as was to be expected from linear gravity wave theory. The height of change (92--93 km) between positive and negative correlation of temperatures and K densities is clearly dominated by the nonlinear layer response, which could be observed largely because of a strong monochromatic gravity wave with vertical wavelength of 30 km and a horizontal period close to 5 hours, quite similar to the predicted nonlinear layer response from theory. These data show that (1) chemical effects are negligible in the response of the K layer to the passage of an atmospheric gravity wave, and (2) that near the peak of the K layer non-linear effects dominate the response. ¿ 1998 American Geophysical Union