In this paper, we consider systems of singularly perturbed integro-differential equations with a rapidly oscillating right-hand side, including an integral operator with a slowly varying kernel. Differential equations of this type and integro-differential equations with slowly varying inhomogeneity and with a rapidly oscillating coefficient at an unknown function are studied. The main goal of this work is to generalize the Lomov’s regularization method and to reveal the influence of the rapidly oscillating right-hand side on the asymptotics of the solution to the original problem.