Control systems are considered which have two saturation non-linearities separated by a linear phase-advance network. Because of the high-pass-filter characteristic of the linear element, distortion produced by the first saturation element is amplified and changes the gain given, to the fundamental component, by the second saturating element. It is shown that the change so caused produces a phase shift through the saturating elements. A joint describing function for the two elements is derived and used to predict sustained oscillations. These oscillations are found to be unstable, and once disturbed, diverge to infinite amplitude. Methods of excitation are examined, and the amplitudes of step functions and sine waves which just excite divergent oscillations are determined. However, the power level of a noise signal which also excites a divergent transient, when applied to the input of the system, is not determined. Analysis of the system when noise is injected into the second saturating element indicates that, in this case, noise has a stabilizing influence.