The equatorial stratospheric wind and temperature fields have been observed by the High-Resolution Doppler Imager (HRDI) and the Microwave Limb Sounder (MLS) instruments, both aboard the Upper Atmospheric Research Satellite (UARS). These independent data sets are analyzed for Kelvin waves through a constrained least squares projection of the data sets onto a basis consisting of Hermite and Fourier functions. This method is developed specifically for HRDI wind measurements since conventional methods do not work well for the irregular nature of HRDI sampling. The recovered eastward spectra from HRDI zonal winds and MLS temperatures are compared for zonal periods from 5 to 10 days per cycle for zonal wavenumbers 1 and 2. The vertical wavelengths of each Kelvin wave event in the two fields compare well. The temperature and the zonal wind fields are not in exact quadrature due to the first-order effects of dissipation, density gradient, and shear. The observed values of zonal wind-temperature correlation and the vertical flux of zonal momentum are studied using a numerical model which involves these first-order effects. ¿ 1998 American Geophysical Union