A short computer program, fully documented, is presented, for the step-by-step dynamic analysis of isolated cables or couples of parallel cables of a cable-stayed bridge, connected to each other and possibly with the deck of the bridge, by very thin pretensioned wires (cross-ties) and subjected to variation of their axial forces due to traffic or to successive pulses of a wind drag force. A simplified SDOF model, approximating the fundamental vibration mode, is adopted for every individual cable. The geometric nonlinearity of the cables is taken into account by their geometric stiffness, whereas the material nonlinearities of the cross-ties include compressive loosening, tensile yielding, and hysteresis stress-strain loops. Seven numerical experiments are performed. Based on them, it is observed that if two interconnected parallel cables have different dynamic characteristics, for example different lengths, thus different masses, weights, and geometric stiffnesses, too, or if one of them has a small additional mass, then a single pretensioned very thin wire, connecting them to each other and possibly with the deck of the bridge, proves effective in suppressing, by its hysteresis damping, the vibrations of the cables.