Several new techniques are developed for identification of linear systems using measurements which are non-linear noninvertible functions of the true plant input and output values. The need for such techniques arises, for example, in applications where power levels rather than amplitude levels are measured, or when transducers must be used for measurement which have even rather than odd transfer characteristics. The analysis, however, is very general and can be directly applied to the identification of any linear plant whose transducer transfer characteristics are decomposable into a finite number of smooth monotonic segments. The development concludes with a recursive identification algorithm and a simple example to demonstrate the method.