We have defined a novel cerebral hemodynamic index, a time constant of the cerebral arterial bed (τ), the product of arterial compliance (C(a)) and cerebrovascular resistance (CVR). C(a) and CVR were calculated based on the relationship between pulsatile arterial blood pressure (ABP) and transcranial Doppler cerebral blood flow velocity. This new parameter theoretically estimates how fast the cerebral arterial bed is filled by blood volume after a sudden change in ABP during one cardiac cycle. We have explored this concept in 11 volunteers and in 25 patients with severe stenosis of the internal carotid artery (ICA). An additional group of 15 subjects with non-vascular dementia was studied to assess potential age dependency of τ. The τ was shorter (p = 0.011) in ICA stenosis, both unilateral (τ = 0.18 ± 0.04 s) and bilateral (τ = 0.16 ± 0.03 s), than in controls (τ = 0.22 ± 0.0 s). The τ correlated with the degree of stenosis (R = -0.62, p = 0.001). In controls, τ was independent of age. Further study during cerebrovascular reactivity tests is needed to establish the usefulness of τ for quantitative estimation of haemodynamics in cerebrovascular disease.