The problem of selecting a suitable high frequency sinusoidal test signal for identification of the parameters in a two-parameter adaptive system is considered. With a sinusoidal test signal it is not possible in general to have a one-to-one independent linear relationship between closed-loop gain and phase shift in terms of the individual parameters. This is due to the large variations in parameters in an adaptive system and due to the practical upper limit on the frequency of the test signal. Retaining the dependence of each of the parameters to both gain and phase shift, a logical method is developed via sensitivity considerations aiming at a. reduction in mathematical computations and obtaining a significant change in phase shift over the entire range of parameters. To illustrate the method two third-order plants each with two varying parameters are considered. Results of analogue computer simulation are given for one of the examples.