SUMMARYMaps of Ertel potential vorticity on isentropic surfaces (IPV) and/or quasi-geostrophic potential vorticity (QGPV) are well established in dynamical meteorology as powerful sources of insight into dynamical processes involving 'balanced' flow. In the present study, we derive maps of zonal-mean IPV and QGPV in Jupiter's upper troposphere and lower stratosphere by making use of a combination of velocity measurements, derived from the tracking of cloud features in images from the Voyager 1 and 2 and Cassini missions, and thermal measurements from the Voyager 1 IRIS and Cassini CIRS instruments. IPV and QGPV are mapped and compared for the entire globe between latitudes ±55 • . Profiles of zonally averaged PV show some evidence for a step-like pattern suggestive of local PV homogenization, separated by strong PV gradients in association with eastward jets, though on differing scales in the northern and southern hemispheres. The northward gradient of PV (IPV or QGPV) is found to change sign in several places in each hemisphere, even when baroclinic contributions are taken into account. The relationship of lateral gradients of IPV and QGPV with the corresponding mean zonal flows indicate that the northern hemisphere may be closer to marginal stability with respect to Arnol'd's second stability theorem than the southern hemisphere.