Cables have been frequently used in many sorts of structure such as bridges, guyed towers, cable-supported roofs, between others. From a structural point of view, cables are flexible and lightly damped and their behaviours may exhibit various dynamical problems. Early studies neglected the inherent nonlinearities of the model that are responsible for the cable vibrations, coupling mode of vibration and cable-deck interaction. In this study, the characteristic dynamic behavior in cable-stayed bridges is analyzed by taking into account the inherent nonlinearities which governs the cable response. The mathematical model consists of a hanging cable between two supports at different heights when is parametrically excited by a sinusoidal displacement in one of the anchorages. It is a simplified model of the vibrations induced by the deck to the cables that belong to a cable-stayed bridge. A parametric study of the cable response is carried out making use of the tools of the Geometric Theory for Dynamical Systems. This work belongs to a general and thorough study that has been carried out by the Departments of Civil Engineering and Mathematical Engineering at the University of Bristol.