Non-linearities affect process identification and linear testing techniques should not be used unless it has been shown that the process is substantially linear within the range of the test signals. A technique is presented which allows extensions of linear identification procedures to be used to identify open-loop processes which contain single-valued non-linearities. It is shown how the effects of the non-linearities may be removed from the output signal, thus allowing identification of the linear dynamics from deterministic signal tests and by random signal cross-correlation techniques. The technique also admits of the determination of that part of the output signal attributable to each power of non-linearity which, in the case of random signal testing, allows the multidimensional impulse responses of the system to be determined independent of the power level of the test signal. It is also shown that, by suitable choice of parameters, the error in the result owing to noise can be made to be no greater than that in the equivalent linear technique.