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The paper contains some results on the existence of solutions for a nonlinear Erd´elyi-Kober fractional quadratic integral equation with deviating arguments. That result is proved under rather general hypotheses. Our equation contains the famous quadratic integral equation of Chandrasekhar type as a special case. The main tools used in our considerations are the concept of measures of noncompactness and the classical Schauder fixed point principle. The investigations of this equation are placed in the Banach space of real functions, defined, continuous and bounded on an unbounded interval. Moreover, we show that solutions of this integral equation are asymptotically stable. We give some examples for indicating the natural realizations of our results presented in this paper.

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