The Milky Way and Andromeda galaxies are the largest members of the Local Group, and their evolution is affected by the evolution of their host as a whole. At the same time, they themselves play an important role in the evolution of the Local Group. Considerable information can be obtained for the Local Group, but little is known about the distances and the full star-formation history of its galaxies. RGB and AGB stars are the keys to trace the full star-formation history of nearby galaxies. These stars are usually the most prominent population of dwarf spheroidal galaxies, but it has been shown (Gallart et al. 1994; Aparicio & Gallart 1994) that they are also observable in dwarf irregular galaxies. This will open the door to the study of the earliest star-formation processes taking place in these galaxies. The star-formation history of the Local Group galaxies is a crucial piece of information for answering basic questions about the evolutionary history of the group.