Data acquired by the Galileo magnetometer on five passes by Ganymede have been used to characterize Ganymede's internal magnetic moments. Three of the five passes were useful for determination of the internal moments through quadrupole order. Models representing the internal field as the sum of dipole and quadrupole terms or as the sum of a permanent dipole field upon which is superimposed an induced magnetic dipole driven by the time varying component of the externally imposed magnetic field of Jupiter's magnetosphere give equally satisfactory fits to the data. The permanent dipole moment has an equatorial field magnitude 719 nT. It is tilted by 176° from the spin axis with the pole in the southern hemisphere rotated by 24° from the Jupiter-facing meridian plane toward the trailing hemisphere. The data are consistent with an inductive response of a good electrical conductor of radius approximately 1 Ganymede radius. Although the data do not enable us to establish the presence of an inductive response beyond doubt, we favor the inductive response model because it gives a good fit to the data using only four parameters to describe the internal sources of fields, whereas the equally good dipole plus quadrupole fit requires eight parameters. An inductive response is consistent with a buried conducting shell, probably liquid water with dissolved electrolytes, somewhere in the first few hundred km below Ganymede's surface. The depth at which the ocean is buried beneath the surface is somewhat uncertain, but our favored model suggests a depth of the order of 150 km. As both temperature and pressure increase with depth and the melting temperature of pure ice decreases to a minimum at ∼170 km depth, it seems possible that near this location, a layer of water would be sandwiched between layers of ice.