Abstract This work studies the dynamic properties and non-linear responses of a sectional model of long-span cable-supported bridge deck under scenarios of resonance with vortex induced vibration or wind fluttering. The cable supported bridge with spatially inclined cables is modeled by a 6-degrees-of-freedom system. The equations of motion for an undamped system are formulated for the study of the effects of inclination angle of cable on the modal parameters. The inclination angle is found strongly affecting the torsional modal frequency of the deck. The equations of motion on the forced excitation of a damped system are also developed for the study of non-linear responses when in resonance. The response analysis is conducted with the Incremental Harmonic Balance method. The inclination angle does not have notable nonlinear effects on the primary resonance of deck heaving response with vertical excitation as the responses of the system are almost identical with those obtained through the linearized model. However, the primary resonance response due to periodic pitching moment indicates an increasing nonlinear effect with an increase in the cable inclination angle. The cables vibrate strongly in both the horizontal and vertical directions with multiple frequency components and non-zero stationary component. The super-harmonic resonance of deck heaving and rotation can only be observed when the damping ratio of system is extremely low.