A new indirect method is proposed to estimate momentum flux based on the theory of slowly varying gravity waves and equatorial waves in vertical shear by Dunkerton which explains the discovery by Sato et al. <1994> that the cospectra of temperature and zonal wind fluctuations at Singapore (1.4 ¿N, 104.0 ¿E) are synchronized with the quasi-biennial oscillation (QBO) of mean zonal wind in the stratosphere. The indirect estimates obtained from cospectra correspond to the summation of absolute values of momentum flux associated with each wave, whereas direct estimates from quadrature spectra give the summation of momentum flux. An analysis was made for twice daily rawinsonde data at Singapore. The direct estimate for Kelvin waves (5--20 day components) is 2-9¿10-3 m2 s-2 and accords with the indirect estimate to within the estimation error. This result supports the validity of the indirect method. Although the indirect estimate depends on an assumed wave structure, large values of momentum flux are obtained for all possible equatorial modes having short periods (1--3 days). The indirect estimate for westerly shear is 20-60¿10-3 m2 s-2 based on the theory of two-dimensional gravity waves, while the direct estimate is only 0-4¿10-3 m2 s-2. The reduction of indirect estimate under the assumption of equatorial waves is about 30--70%. The discrepancy between direct and indirect estimates indicates a large cancellation of positive and negative momentum fluxes. This is the case also for easterly shear. The indirect estimate for westerly shear is almost twice as large as that for easterly shear. The characteristics of waves near the source in the troposphere are thought to be independent of the QBO in the stratosphere, so that the difference in wave activity should be attributed to the differing characteristics of wave propagation under the strong QBO shear. Several possible explanations are discussed. Parameters such as phase velocity and zonal wavelength are estimated from the ratio of potential to kinetic energies assuming that the 1--3 day components are due to equatorial waves. The estimates in this paper were made assuming that the observed frequencies are actual ground-based wave frequencies. If there is aliasing from higher frequencies than 1 day, the actual momentum fluxes can be significantly larger than the estimated values. ¿ 1997 American Geophysical Union