The regulation of cerebral blood flow (CBF) following changes in arterial blood pressure (ABP) and end-tidal pCO2 (EtCO2) are of clinical interest in assessing cerebrovascular reserve capacity. Linear finite-impulse-response modelling is applied to ABP, EtCO2 and CBF velocity (CBFV, from transcranial Doppler measurements), which allows the CBFV response to ideal step changes in EtCO2 to be estimated from clinical data showing more sluggish, and additional random variations. The confounding effects of ABP changes provoked by hypercapnia on the CBFV are also corrected for. Data from 56 patients suffering from stenosis of the carotid arteries (with normal or diminished cerebrovascular reactivity to EtCO2 changes--CVRCO2) were analysed. The results show the expected significant differences (p < 0.05) between EtCO2 steps up and down, the significant contribution from ABP variation, and also differences in the dynamic responses of patients with reduced CVRCO2 (p < 0.01 after 10 s). For the latter the CBFV response appears exhausted after about 15 s, whereas for normals CBFV continues to increase. While dispersion of individual step responses remains large, the method gives encouraging results for the non-invasive study of compromised haemodynamics in different patient groups.