Westward and eastward propagating tropical waves in total ozone are investigated in 13 years (1979--1991) of version 6 total column ozone data from the Nimbus 7 total ozone mapping spectrometer (TOMS) satellite instrument. A clear synchronization between the stratospheric quasi-biennial oscillation (QBO) zonal winds and the fast (periods < 15 days) propagating waves in tropical TOMS data is detailed. Largest total ozone wave amplitudes (approx. 3--6 Dobson units) occur when their phase propagation direction is primarily opposite the Singapore QBO lower-stratospheric winds. This effect is most apparent in meridionally symmetric components. Examination of specific episodes, including cross-spectral calculations with Singapore rawinsonde wind data (10--70 hPa), reveals signatures of tropically confined eastward propagating Kelvin waves of zonal wavenumbers 1-2 during the descending eastward QBO phase, consistent with acceleration of that QBO phase by Kelvin waves. The TOMS results are also consistent with possible forcing of the westward QBO wind phase by episodes of both meridionally symmetric and asymmetric westward waves (W' events in the text). However, in contrast to the case of eastward (Kelvin) waves the strongest westward events (W events in the text) appear to be filtered by, rather than forcing, the westward phase of the stratospheric QBO wind. These dominant westward episodes are interpreted as meridionally symmetric westward global normal modes and tropically confined equatorial-Rossby waves 2--6. The events exhibit phase and group speeds characteristic of wave dynamics rather than simple wind advection. These results underscore the utility of the long time series and excellent horizontal coverage of TOMS data for dynamical investigations in the relatively observation-poor tropical stratosphere.