We consider the distribution of plasma density in the atmosphere of Ganymede and present electron density profiles inferred from data of the Plasma Wave instrument of Galileo. To study the question of ionospheric plasma, we present a zero-dimensional local rate equation model of the source and loss functions and the atomic and molecular processes we assume to be taking place. We conclude from the model that Ganymede has a bound ionosphere composed mainly of molecular oxygen ions in the polar regions and of atomic oxygen ions at low latitudes and that protons are absent everywhere. This implies that the plasma observed to be flowing out along the open flux tubes connected to the polar cap is composed of ions of atomic oxygen. We predict that Ganymede is surrounded by a corona of hot oxygen atoms. The model neutral atmosphere has a composition similar to that of the ionosphere and is exospheric everywhere. Our calculated neutral column density is consistent with values of Ganymede ultraviolet auroral brightness observed by means of the Hubble Space Telescope.