Interest in dwarf spheroidal galaxies is motivated by a number of reasons; an important one on the occasion of this colloquium is the abundance of variable stars. The theory of stellar evolution and stellar pulsations is now able to predict from theoretical considerations characteristic properties of variable stars in the colour-magnitude diagram (Iben, 1971). By observing the variable stars in the field, and in as wide a selection of objects as possible, more insight can be obtained into the history of the oldest members of our Galaxy (the globular clusters) and of the dwarf spheroidal galaxies in the Local Group. It is worthwhile to explore the spheroidal galaxies as observational tests for the theoretical predictions of conditions in space away from our Galaxy. The numbers of variable stars in the dwarf spheroidal galaxies are such that we may expect well-defined relations to emerge once reliable magnitude sequences have been set up, the variable stars found, and their periods determined. Six dwarf spheroidal galaxies are presently known in the Local Group within a distance of 250 kpc. In Table I, which lists members of the Local Group, they are at the low-luminosity end of the sequence of elliptical galaxies (van den Bergh, 1968).