  In the resonance model, high-frequency quasi-periodic oscillations (QPOs) are
supposed to be a consequence of nonlinear resonance between modes of
oscillations occurring within the innermost parts of an accretion disk. Several
models with a prescribed mode--mode interaction were proposed in order to
explain the characteristic properties of the resonance in QPO sources. In this
paper, we examine nonlinear oscillations of a system having a quadratic
nonlinearity and we show that this case is particularly relevant for QPOs. We
present a very convenient way how to study internal resonances of a fully
general system using the method of multiple scales. Finally, we concentrate to
conservative systems and discuss their behavior near the 3:2 resonance.
