Context. There is a need in some research facilities for deriving ephemerides, controlling observations, verifying various models of motion, and calculating the coordinates in space of natural planetary satellites. Aims. The goal of our work is to elaborate the ephemerides of all natural satellites based upon all observations available to date and readily accessible for any user via the Internet. Methods. For all outer planetary satellites, original numerical models of motion are used that are based on all published observations. For other satellites, the theoretical models of the motion are taken from publications that are as recent as possible. Complete collection of the theories and models of motion is realized as a software for the ephemerides of natural satellites available on the web pages of the so-called server MULTI-SAT. Results. A new facility for producing ephemerides of all natural satellites of planets (except the Moon) has been created at IMCCE and SAI. Special features of the ephemerides are realized, such as predicting the phenomena and providing configurations useful for the observers. The server MULTI-SAT is accessible through the Internet. The URL addresses are http://www.imcce.fr/sat (English and French versions at IMCCE) and http://www.sai.msu.ru/neb/nss/index.htm (English, French, and Russian versions at SAI). This paper includes a complete review of the most precise theories of motion of all natural satellites that we used and an analysis of the precision of the proposed ephemerides.