Mayr et al. discussed a two-dimensional version of the numerical spectral model (NSM) of Chan et al. <1994a, b> that incorporates the Doppler spread parameterization (DSP) for momentum deposition by small-scale gravity waves (GW) developed by Hines <1997a, b> and presented numerical results describing the global scale seasonal variations in the temperature and wind fields of the middle atmosphere. Even with the simplest assumptions for the GW flux emanating from the troposphere, to be isotropic and independent of latitude and season, this model also produces significant oscillations in the equatorial zonal circulation which are discussed here. Our model results lead to the following conclusions: (1) At altitudes above 40 km, a periodicity of 6 month dominates, resembling the observed semiannual oscillation (SAO). The peak amplitude of this oscillation is close to 18 m/s near 50 km (20--30 m/s observed). A secondary maximum is excited near 80 km with an amplitude of about 11 m/s (15--25 m/s observed), whose phase is opposite to that at 50 km. In this altitude range, the downward phase progression is about 9 km/month, in agreement with observations. The computed SAO is confined to equatorial latitudes, as observed. (2) At altitudes below 40 km, the period of the computed oscillation is almost 21 months, approaching that of the observed quasi-biennial oscillation (QBO). The maximum wind amplitudes are close to 8 m/s (20 m/s observed), and the downward phase progression is about 1.6 km/month (1.3 km/month observed). The model also produces a QBO in the upper mesosphere, in qualitative agreement with recent UARS measurements <Burrage et al., 1996>. (3) When the eddy diffusivity is reduced by a factor of two, the QBO period increases to 30 months and the maximum wind amplitude approaches 13 m/s. Computer experiments are discussed for constant, equinoctial solar heating to elucidate the GW excitation mechanism for the equatorial oscillations in the zonal circulation. ¿ 1997 American Geophysical Union