Dust measurements have been obtained with the dust detector onboard the Galileo spacecraft inside a distance of about 60RJ form Jupiter (Jupiter radius, RJ=71,492 km) during two periods of about 8 days around Galileo's closest approaches to Ganymede on 27 June and on 6 Sept 1996. The impact rate of submicrometersized particles fluctuated by a factor of several hundred with a period of about 10 hours, implying that their trajectories are strongly affected by the interaction with the Jovian magnetic field. Concentrations of small dust impacts were detected at the times of Ganymede closest approaches that could be secondary ejecta particles generated upon impact of other particles onto Ganymede's surface. Micrometer-sized dust particles, which could be on bound orbits about Jupiter, are concentrated in the inner Jovian system inside about 20RJ from Jupiter.¿ 1997 American Geophysical Union