Abstract
<abstract> In the paper we are going to prove the existence of solutions of an infinite system of nonlinear quadratic integral equations of Volterra-Hammerstein type. Those solutions are continuous and bounded functions defined on the real half-axis $ \mathbb{R}_+ $ and created by function sequences which are coordinatewise converging to proper limits at infinity. Considerations of the paper are located in the Banach space consisting of functions defined, continuous and bounded on $ \mathbb{R}_+ $ with values in the space of real bounded sequences. The main tool applied in the paper is the technique of measures of noncompactness. </abstract>
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