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<p/> <p>We investigate the mild solutions of a nonlocal Cauchy problem for nonautonomous fractional evolution equations <inline-formula><graphic file="1687-1847-2011-483816-i1.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2011-483816-i2.gif"/></inline-formula>, in Banach spaces, where <inline-formula><graphic file="1687-1847-2011-483816-i3.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2011-483816-i4.gif"/></inline-formula>. New results are obtained by using Sadovskii's fixed point theorem and the Banach contraction mapping principle. An example is also given.</p>