Cable-stayed bridges frequently experience vibrations due to a variety of mechanisms, exacerbated by their very low inherent damping. A research group of the University of Bristol has focused lately on the study of cable-stayed bridges, some advances have led to the identification of vortex-induced deck vibrations occurring at the Second Severn Crossing (SSC) and improved methods of analysis of field vibration data. Based on such experience, it aims to study the autoparametric excitation which, due to very great amplitudes, can seriously damage the structure. It has been suggested that this may have been the mechanism of excitation of some large amplitude cable vibrations on real bridges, but the details of the behaviour are not very well understood and several cases of large cable vibrations on full scale bridges have not been fully explained. In this paper we examine a previously established cable-deck model and compare it to a new, more exact model in a different coordinate basis.