In this paper, we give first a contribution to the ‘dual input describing function’ of Westet al.(1956); we show how it is possible to define by means of the characteristic curve of the non-linearity alone, without knowing the mathematical expression for it. Secondly, we give a new method for determining the self-oscillation of a non-linear system dependent on reactive energy considerations. Lastly, we extend the theory to non-linear multivariable systems.