FRAM (F/Photometric Robotic Atmospheric Monitor) is a robotic telescope operated at the Pierre Auger Observatory in Argentina for the purposes of atmospheric monitoring using stellar photometry. As a passive system which does not produce any light that could interfere with the observations of the fluorescence telescopes of the observatory, it complements the active monitoring systems that use lasers. We discuss the applications of stellar photometry for atmospheric monitoring at optical observatories in general and the particular modes of operation employed by the Auger FRAM. We describe in detail the technical aspects of FRAM, the hardware and software requirements for a successful operation of a robotic telescope for such a purpose and their implementation within the FRAM system.La lista completa de autores puede verse al final del archivo asociado.Instituto de Física La Plata