Systems containing two non-linearities separated by a stabilizing network of the formSand (1 + τS) are considered. The input to the second non-linear block is not a pure sinusoid but contains all higher harmonics. An equivalent non-linear characteristic is found which changes with frequency and amplitude, and a joint describing function is obtained. The method is believed to be novel and is applicable even if one non-linearity is of the backlash type.