The output of a non-linear element subjected to two sinusoidal signals of incommensurate frequencies is almost periodic. An exact method of determining the complete response, that is, the amplitudes of the fundamental, harmonic and combination frequencies of the two signals at the output has been developed. A special virtue of this analysis is that it can be carried out graphically or numerically if the non-linear characteristic cannot be expressed in an analytical form or if the resulting integrals are difficult to evaluate. The application of the method is illustrated by deriving expressions for the fundamental, harmonic and combination frequency components in the output of specific non-linearities. This analysis also shows that the approximate DIDF of Oldenburger and Boyer for signals of widely different frequencies is, in fact, the exact DIDF for signals of incommensurate frequencies.