Nonlinear distortion

Nonlinear distortion is a term used (in fields such as electronics, audio and telecommunications) to describe the phenomenon of a non-linear relationship between the "input" and "output" signals of - for example - an electronic device. 
Model.
For many devices, a linear model is accurate only for small signal levels. For example, at 2 volts input, a typical audio amplifier might put out 20 V, meaning the linear gain is 10 V/V. For 3 V input, it might then output 30 V. However, the model implies that at 50 V input it would produce 500 V, which is not possible with most amplifiers.
Mathematically, the input-output relationship of many devices should be described by a polynomial or Taylor series, as shown below.
formula_1
For larger values of "u", the higher order coefficients such as formula_2 and formula_3 come into play.
Effects of nonlinearity.
Nonlinearity can have several effects, which are unwanted in typical situations. The formula_3 term for example would, when the input is a sine wave with frequency formula_5, result in an extra sine wave at formula_6, as shown below.
formula_7
In certain situations, this spurious signal can be filtered away because the "harmonic" formula_6 lies far outside the frequency range used, but in cable television, for example, third order distortion could cause a 200 MHz signal to interfere with the regular channel at 600 MHz. 
Nonlinear distortion applied to a superposition of two signals at different frequencies causes the circuit to act as a frequency mixer, creating intermodulation distortion.