The electrodynamical interaction between Jupiter and comet Shoemaker--Levy 9, which is expected to impact on Jupiter around July 20, 1994, is investigated. The comet consists of a sequence of 21 or so nuclei, each surrounded by a neutral cloud of outgassed material. A model is constructed of one single such cloud which is subject to electron impact ionization during the passage through Jupiter's magnetosphere. The cloud is assumed to couple electrically to the surroundings either by means of Alfv¿n wings, or through a dc circuit that closes in Jupiter's ionosphere. The magnetic-field-aligned currents resulting from the Jupiter--Io interaction are strongly connected to the Jovian Decametric Radiation. The Shoemaker--Levy comet can theoretically supply ions to Jupiter's magnetosphere at a rate not so far below Io's, and will have a higher velocity relative to Jupiter, and could therefore conceivably drive similar processes. However, we find that, due to the high latitude trajectory of the comet, the resulting currents become very weak. The field-aligned currents obtained in this study are a factor 500 below those driven by Io, while the dissipated power is almost a factor 106 below. It is therefore proposed that very little or no detectable electromagnetic radiation will arise during the comet's passage through Jupiter's magnetosphere. ¿ American Geophysical Union 1994