Starting from July 1992, the apparent inclination of the orbital plane of the satellites of Saturn has begun to be small enough to induce phenomena. This configuration occurs every 15 years and gives the opportunity to observe eclipses and occultations of the first eight Saturnian satellites by the planet. Moreover, in 1995 and 1996, the Earth and Sun will pass through the plane of the rings and we will also observe mutual events of the Saturnian satellites: the satellites will eclipse and occult one another. We have computed the whole set of these phenomena and we give in this paper a selected set of eclipses by the planet and mutual events which could be observed under the best conditions: we will observe 163 eclipses by Saturn from 1993 May to 1996 August and 182 mutual eclipses and occultations from 1995 January to 1996 September. The observation of this type of event gives the opportunity to get astrometric measurements with a very high precision and will permit us to improve our knowledge of the dynamical motion of these satellites. Furthermore these observations are an interesting method for physical investigations concerning the atmosphere of Saturn or Titan, and they can he used for a photometric study of the surface scattering. We will organize a campaign and we call for observations of eclipses of the satellites by Saturn and for observations of their mutual events.