Analysis of various characteristics of the statistical spectra of total ozone covering a 15 year period (1964--1978), and of ozone in the stratosphere over a period of about 7 years, indicates that the strong QBO in the zonal winds of the tropical stratosphere is associataed with a detectable, although often weak, signal in total ozone and the ozone concentration in the lower and middle stratosphere. The region of strongest relationship between tropical stratospheric zonal winds and total ozone (e. g., maximum ozone associated with strong west winds) is in the tropics, midlatitudes of the southern hemisphere, and, apparently, at high latitudes of the northern hemisphere. The observed period of the ozone QBO decreases from 27 months at the equator to about 24 months in mid-latitudes possibly due to local modification of the QBO, as it propagates poleward. In the tropics the ozone variation appears to be nearly in phase wiht the tropical wind QBO while at middle and high latitudes of the northern hemisphere and mid-latitudes of the southern hemisphere the ozone oscillation seems to lag the wind oscillation by about 12--14 months. The out-of-phase relationship at middle and high latitudes suggests a possible interaction between the tropical stratosphere QBO in zonal winds and the annual variation in poleward transport of ozone by quasi-horizontal eddies.