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We consider evolution of interstellar clouds in Local Group dwarf spheroidalgalaxies (dSphs) in the context of their observed star formation histories. TheLocal Group dSphs generally experienced initial bursts of star formations intheir formation epochs ($\sim 15$ Gyr ago), when hot gas originating from thesupernovae can make the cold interstellar clouds evaporate. We find that themaximum size of evaporating cloud is 10 pc. Thus, clouds larger than 10 pc cansurvive during the initial star formation. These surviving clouds cancontribute to the second star formation to produce ``intermediate-age ($\sim$3--10 Gyr ago) stellar populations.'' Assuming that collisions between cloudsinduce star formation and that the timescale of the second star formation is afew Gyr, we estimate the total mass of the clouds. The total mass is about$10^{4}M_\odot$, which is 1--3 orders of magnitude smaller than the typicalstellar mass of a present dSph. This implies that the initial star formation isdominant over the second star formation, which is broadly consistent with theobserved star formation histories. However, the variety of the dSphs in theirstar formation histories suggests that the effects of environments on the dSphsmay be important.Comment: 14 pages LaTeX, no figures, to appear in Ap

Evolution of Interstellar Clouds in Local Group Dwarf Spheroidal Galaxies in the Context of Their Star Formation Histories