Non-linear hearing instruments, by definition, adapt their signal-processing characteristics depending on the input signal. For clinical purposes we propose the following six basic manufacturer-independent specifications for all hearing instruments with single- or multi- channel AGC, using any recorded real-life sound as test signal: (a) A typical gain frequency response, in a given environment, is estimated as the time-average of the log magnitude (dB) of short-time frequency responses, with a frequency resolution equal to auditory equivalent rectangular bandwidths (ERB); (b) A typical group delay response, in a given environment, is estimated as the time-average of short-time group delay responses; (c) Between-environment adaptation (slow AGC) is shown by the relation between typical gain frequency responses in different sound environments; (d) Within-environment adaptation (fast AGC) is efficiently shown by input-output scatter plots of just four ERB cepstrum coefficients; (e) Effective within-environment compression ratios are derived by vector quantization of the statistical distribution of input and output ERB cepstrum coefficients; and (f) A time-frequency display of short-time gain frequency responses effectively illustrates the temporal adaptation characteristics. We have analysed the performance of four modern non-linear hearing aids using a recorded conversation in traffic noise as test signal. The results show astonishingly large differences between the hearing instruments. The analysis is feasible with a normal personal computer.