Large variations are observed in the Semi-Annual Oscillation (SAO) and Quasi-Biennial Oscillation (QBO) near the equator that are not well understood. We had shown earlier that small scale gravity waves (GW) can generate these oscillations. Here we demonstrate that GW filtering can also produce the variability. Our model incorporates Hines' Doppler Spread Parameterization (DSP) for GW. In the present version, we employ a larger GW flux and a more realistic description of Newtonian cooling. This model produces a QBO with amplitudes close to 15 m/s at 25 km and periods around 33 months. At higher altitudes, the model produces a SAO with amplitudes varying between 5 and 30 m/s. We interpret these variations in terms of GW filtering by the QBO that produces beat periods between 4 and 8.5 years. To provide better understanding, we present also a case in which the QBO period is virtually locked at 18 months. The SAO amplitude then varies with a regular pattern having a period of 18 months, and the Annual Oscillation (AO) amplitude varies with a period of 36 months. For QBO's with periods of 18 (or 30) months, the phase relationship with the seasonal cycle of solar forcing would tend to synchronize and stabilize the oscillations. ¿ 1998 American Geophysical Union