From 1992 to 1999, the satellites of Saturn are involved in several phenomena: eclipses or occultations by the planet, transits in front of Saturn, or transits of their umbra. These phenomena occur thanks to the geometrical circumstances in 1995 when the Earth and the Sun went through the plane of the Saturnian ring and consequently through the orbital planes of the main satellites. These circumstances are also favorable to the observation of mutual phenomena occurring when the satellites eclipse or occult each other. These mutual phenomena and the eclipses by Saturn are rare as they occur only every 15 years. But, they are very useful to get highly accurate astrometric observations and they allowed us to estimate some physical parameters. We have organized the PHESAT95 campaign to observe these phenomena and a special effort was made to observe as many events as possible. At the present time, the observations are still being collected from different teams and different countries; this paper shows the first results which have been obtained in several sites, and the first comparison with the theory of the motions.