The Earth's equatorial stratosphere shows oscillations in which the east-west winds reverse direction and the temperatures change cyclically with a period of about two years. This phenomenon, called the quasi-biennial oscillation, also affects the dynamics of the mid- and high-latitude stratosphere and weather in the lower atmosphere. Ground-based observations have suggested that similar temperature oscillations (with a 4-5-yr cycle) occur on Jupiter, but these data suffer from poor vertical resolution and Jupiter's stratospheric wind velocities have not yet been determined. Here we report maps of temperatures and winds with high spatial resolution, obtained from spacecraft measurements of infrared spectra of Jupiter's stratosphere. We find an intense, high-altitude equatorial jet with a speed of approximately 140 m s(-1), whose spatial structure resembles that of a quasi-quadrennial oscillation. Wave activity in the stratosphere also appears analogous to that occurring on Earth. A strong interaction between Jupiter and its plasma environment produces hot spots in its upper atmosphere and stratosphere near its poles, and the temperature maps define the penetration of the hot spots into the stratosphere.