In this paper 1 review the reasons why it is desirable to place a remote-sensing satellite into an orbit which periodically repeats its path. Such exactly-repeating orbits are often used for Earth remote-sensing satellites, but the most appropriate orbit depends upon the likely application of the data. If they are to be used to study a rapidly changing phenomenon a short repeat period is obviously preferable, whereas if a dense grid of subsatellite tracks is required (e.g., for a large mapping project) a long repeat period is required. The increasing tendency to design multi-purpose remote sensing satellite missions means that these requirements are more likely to come into conflict. 11 is however sometimes possible to choose an orbit which, while exactly repeating itself only after a long period, almost repeats itself at much shorter intervals. These orbits are often called orbital subcycles or drifting subcycles and this paper sets out their theory in sufficient detail, it is hoped, to enable remote sensing scientists lo assist space agencies in selecting orbits which satisfy as many users as possible.