Amateur observations made since 1977 show that although the ephemerides for the satellites of Jupiter published by the Jet Propulsion Laboratory are more accurate than those in the Astronomical Almanac, there are still small deviations, which may increase with time. Observation of eclipses, transits and occultations, as well as of the mutual phenomena that occur at 6-yearly intervals can provide information for correction of the ephemerides. There appear to be three groups coordinating observations: 1) in Germany, started by P. Ahnert in the early 1960s and now under H.-J. Blasberg; 2) in the U.S.A., started by J. Ashbrook in 1976, and continued by J. Westfall of the ALPO; 3) in Australia and New Zealand, led by B. Loader. These groups appear to work independently, and it would greatly help research on this subject if there were an International Centre for collecting observations of the Jovian satellites – perhaps under the supervision of the IAU – whereby all observations made anywhere in the world would be available to anyone investigating the subject. Paris, where the predictions are calculated, might be a very suitable site for such a centre.