In this presentation systems of weakly coupled nonlinear oscillators will be discussed. These systems are widely used to model nonlinear resonance phenomena such as autoparametric resonance. This is of particular importance in modelling very lightly damped physical systems, such as strings, cables, flexible beams, membranes, plates, shells and rotating blades. The fact that the natural damping in the structure is very small means that, firstly, there are very large displacement amplitude responses at a resonance (usually undesirable for the design of the structure), and second, the damped response is very close to the undamped response. As a result the most important characteristics of the system can by understood from the resonances of the system. The undamped resonance behaviour can be defined by a series of backbone curves, and we will describe how these curves can be obtained for two examples of coupled nonlinear oscillators. The first example is a two mass oscillator system. The second example will relate to whirling motion in a taut cable.