A mathematical model is described that demonstrated the properties of cerebral vascular resistance and compliance expressed as a function of cerebral perfusion pressure (CPP) and arterial CO2 partial pressure (PaCO2). The hypercapnic induced shift of the lower limit of autoregulation to a higher range of CPP, as shown by this model, is a useful characteristic that facilitates the differentiation between normal and impaired autoregulation described previously in experimental studies. Dynamic properties of cerebrovascular circulation derived from the relationship between pulse wave of CBF waveform and CPP have been analysed at different levels of PaCO2-phenomenon, being often described as dependence of blood flow velocity pulsatility index on the autoregulatory reserve. The model was also used to interpret interhemispheric asymmetry of CBF reactivity to changes in arterial concentration of CO2 in patients with carotid artery stenosis.