Galileo, as the first orbiting spacecraft in an outer planet's magnetosphere, provides the opportunity to study global energetic ion distributions in Jupiter's magnetosphere. We present directional anisotropies of energetic ion distributions measured by the Galileo Energetic Particles Detector (EPD). The EPD measurements of proton (80--1050 keV), oxygen (26--562 keV/nucleon), and sulfur (16--310 keV/nucleon) distributions cover a wide energy range. Spatially, the data set includes measurements from 6 to 142 Jovian radii (RJ) and covers all local times inside the Jovian magnetosphere. For each species a single detector head scans almost the entire sky (≈4&pgr; sr), producing the three-dimensional angular distributions from which the anisotropies are derived. Consequently, the resulting anisotropy estimates are both global and robust. Such anisotropies, generally produced by convective flow, ion intensity gradients, and field-aligned components, have long been used to estimate flow velocities and to locate spatial boundaries within magnetospheres. They can therefore provide vital information on magnetospheric circulation and dynamics. We find that the EPD measured anisotropies in the Jovian magnetosphere are dominated by a component in the corotational direction punctuated by episodic radial components, both inward and outward. Under the assumption that anisotropies are produced predominantly by convective flow, we derive flow velocities of protons, oxygen ions, and sulfur ions. The validity of that approach is supported by the fact that these three independently derived flow velocities agree, to a large extent, in this approximation. Thus, for the first time, we are able to derive the global flow pattern in a magnetosphere of an outer planet. In a comparison between the first-order EPD flow velocities and those predicted by a magnetohydrodynamic (MHD) simulation of the Jovian magnetosphere, we find that qualitatively the directions appear similar, although no firm evidence of steady outflow of ions has been observed at distances covered by Galileo. A first rough comparison indicates that the measured first-order flow velocities are higher by at least a factor of 1.5 than the MHD simulation results. ¿ 2001 American Geophysical Union