The present paper describes a new method to estimate the auditory brainstem response when the electrical activity from the recording electrodes displays non-stationarity, i.e. varies between low and high levels. The method is based on a statistical approach called Bayesian inference and weights the individual components (here blocks of 250 sweeps) inversely proportional to the level of the noise activity during the recording. Fifty sets of data from 10 consecutive patients obtained during stimulation at high intensity are used to evaluate the difference between the classic averaging and the present method which is called Bayes estimation. In approximately 30% of the cases, a significant all-over improvement is obtained by the new method. The classic averaging technique would here require 50% more sweeps to be taken to obtain the same precision of the ABR estimate, on average. Also the latency and amplitude parameters of the Jv wave complex are evaluated and it is shown that the parameter variance decreases by a factor of approximately 2 by using the Bayes estimation. The new technique is compared with a similar technique recently presented by Hoke et al. (1984) and the differences and similarities are discussed.