Abstract : We have developed a new dynamical model of the Galilean system fitted to astrometric observations. A numerical code has been developed for simulating the orbital motion of the satellites. Many perturbations usually neglected have been quantified, improving greatly the modeling of the system. The numerical solution has been fitted to various kinds of observations (photographic, CCD and mutual phenomena) done between 1891 and 2002. More than 2000 observations have been used, including the PHEMU campaigns of 1985 and 1991. A frequency analysis was finally used to obtain an orbital representation under an analytical form. A digital filtering treatment for removing the short periods from the long ones has been developed, hence solving some technical problems such as the length of the sample and the long solar periods. Our theory has an accuracy of a few tens of kilometres over one century and remains valid for more than 1500 years.