Summary: The main aim of this work is to study the existence of \(S\)-asymptotically \(\omega\)-periodic solutions for a class of abstract integro-differential equations modeled in the following form \[ \begin{aligned} \frac{d}{dt} [x(t) + \int_0^t N(t - s) x(s) ds] & = Ax(t) + \int_0^t B(t - s) x(s) ds + f(t, x(t)),\quad t \geqslant 0, \\ x(0) & = x_0 \in X, \end{aligned} \] where \(A, B(t)\) for \(t \geqslant 0\) are closed linear operators defined on a common domain \(D(A)\) which is dense in \(X, N(t)\) for \(t \geqslant 0\) are bounded linear operators on \(X\), and \(f : [0, \infty) \times X \to X\) is an appropriate function. The existence results are obtained by applying the theory of exponentially stable resolvent operators. We also discuss an application of these results.