The classical two-degree-of-freedom (2-d-o-f) "sectional model" is currently used to study the dynamics of suspension bridges. Taking into account the first pair of vertical and torsional modes of the bridge, it describes well global oscillations caused by wind actions on the deck and yields very useful information on the overall behaviour and the aerodynamic and aeroelastic response, but does not consider relative oscillation between main cables and deck. The possibility of taking into account these relative oscillations, that can become significant for very long span bridges, is the main purpose of the 4-d-o-f model, proposed by the Authors in previous papers and fully developed here. Longitudinal deformability of the hangers (assumed linear elastic in tension and unable to react in compression) and external loading on the cables are taken into account: thus not only global oscillations, but also relative oscillations between cables and deck can be described. When the hangers go slack, large nonlinear oscillations are possible; if the hangers remain taut, the oscillations are small and essentially linear. This paper describes the model proposed for small and large oscillations, and investigates in detail the limit condition for linear response under harmonic actions on the cables (e.g., like those that could be generated by vortex shedding). These results are sufficient to state that, with geometric and mechanical parameters in a range corresponding to realistic cases of large span suspension bridges, large relative oscillations between main cables and deck cannot be excluded, and therefore should not be neglected in the design. Forthcoming papers will investigate more general cases of loading and dynamic response of the model.