The presence of parametric excitation is one of the possible excitation mechanisms with as iconic example the Mathieu-equation. It is often used for describing a pendulum with oscillating support, but the equation comes up in many applications. A basic element is the calculation of instability tongues in force of excitation-frequency space. More complex applications are concerned with nonlinear interaction with other oscillators and the study of flow-induced vibrations, see also Chap. 12 . Autoparametric systems are using parametric oscillators as energy absorbers. An example is quenching of Rayleigh self-excited oscillations.