A mathematical model of cerebral blood flow and the cerebrospinal fluid circulation is described which permits the study of phenomena caused by dynamic changes in cerebrovascular autoregulatory or cerebrospinal fluid compensatory reserves. A transient decrease in cerebral perfusion pressure was produced by carotid artery compression. Comparison of the computer simulations with clinical and experimental data, reported elsewhere, suggests that the transient hyperaemic response (THR) is proportional to the strength of the autoregulatory response. The relationships between the magnitude and time course of the THR, and the period and level of reduction in CPP were studied. This model suggests that simple clinical tests based on the examination of THR using transcranial Doppler velocity measurements are of potential value for the non-invasive assessment of the autoregulatory reserve.