Ultralow-frequency (ULF) pulsations are an important class of phenomena characterizing the dynamics of the terrestrial magnetosphere and are usually interpreted as standing magnetohydrodynamic waves in the magnetospheric plasma of planet Earth. Spacecraft observations indicate that the Hermean and Jovian magnetospheres also support such eigenoscillations. Whether ULF waves exist in the magnetosphere of the planet Saturn is the topic of this work. On the basis of a simple plasma mass distribution model, periods of Kronian eigenoscillations are estimated. Values comparable to the planetary rotation period are found, which makes the existence of standing waves improbable. Despite this significant difference in Earth's magnetosphere it is shown that this does not inhibit the resonant coupling between fast mode type magnetopause surface waves and local propagating Alfv¿n modes. Against this background we examine a pattern in the magnetic field data recorded by Voyager 1 during its encounter with Saturn. The analysis of the pattern and a modeled satellite crossing give indications that resonant mode coupling was detected. ¿ 1998 American Geophysical Union