For about 25 years the Jovian magnetosphere is known to be a strong source of electrons with energies up to ~30 MeV. Many in-situ observations have not only confirmed this finding originally made with the Pioneer 10 spacecraft, but have also revealed that the Jovian electrons appear to be present, at least close to the ecliptic plane, in the distance range from 0.5 to 25--30 AU. The growth of the observational basis was not accompanied by any comparable progress with the modelling of the propagation of Jovian electrons. The few existing models suffer from the restriction to be valid either only very close to or far away from the source region. They are, therefore, not exploitable for a detailed study of the observations, in particular of those made with the Ulysses spacecraft during the last nine years. Motivated by this situation we have developed a new model of the propagation of both Jovian and galactic electrons. We present first simulation results and comment on their potential value for distinguishing between Jovian and galactic electrons, for bracketing the range of the possible interstellar electron fluxes at low energies, and for a determination of the diffusion tensor of low-energy electrons (>1 MeV) in the heliosphere. ¿ 2000 American Geophysical Union