A global array of 20 radio observatories was used to measure the three-dimensional position and velocity of the two meteorological balloons that were injected into the equatorial region of the Venus atmosphere near Venus midnight by the VEGA spacecraft on 11 and 15 June 1985. Initial analysis of only radial velocities indicates that each balloon was blown westward about 11,500 kilometers (8,000 kilometers on the night side) by zonal winds with a mean speed of about 70 meters per second. Excursions of the data from a model of constant zonal velocity were generally less than 3 meters per second; however, a much larger variation was evident near the end of the flight of the second balloon. Consistent systematic trends in the residuals for both balloons indicate the possibility of a solar-fixed atmospheric feature. Rapid variations in balloon velocity were often detected within a single transmission (330 seconds); however, they may represent not only atmospheric motions but also self-induced aerodynamic motions of the balloon.