Summary: The paper deals with the study of the existence of solutions of a quadratic integral equation of Volterra-Stieltjes type. We are looking for solutions in the class of real functions continuous and bounded on the real half-axis \(\mathbb{R}_+\) and converging to proper limits at infinity. The quadratic integral equations considered in the paper contain, as special cases, a lot of nonlinear integral equations such as the Volterra-Chandrasekhar or the Volterra-Wiener-Hopf equations, among others. In our investigations we use the technique associated with measures of noncompactness and the Darbo fixed point theorem. Particularly, we utilize a measure of noncompactness related to the class of functions in which solutions of the integral equation in question occur.