The nonproportional relationship between instantaneous arterial blood pressure (BP) and cerebral blood flow velocity (CBFv) is well explained by the concept of critical closing pressure (CCP). We aimed to determine the frequency response of the neonatal cerebrovascular system, and to establish the exact mathematical relationship between cerebrovascular impedance and CCP under physiologic conditions. In 10 preterm neonates (gestational age, 25-32 weeks; birth weight, 685-1,730 g; age 1-7 days) we Doppler-traced CBFv of the internal carotid artery. Blood pressure was traced simultaneously. Critical closing pressure was graphically determined. Cerebrovascular impedance was calculated as the square root of the ratio of the corresponding peaks in the power spectra of BP and CBFv at zero frequency, and at heart rate (H) and harmonics (xH). Uniformly, the impedance between H and 3H (2 to 6 Hz) was reduced about fivefold, compared with the impedance at zero frequency. The cerebrovascular system behaves like a high-pass filter, leading to a reduction of the DC (direct current) component of CBFv (analogous to current) relative to that of the driving force BP (analogous to voltage). The frequency response of cerebrovascular impedance reflects the ratio of CCP and DC BP. A mathematical derivation of this relationship is given matching the observed results. Thus, both the CCP and the impedance approach are valid.