To determine the dynamic characteristics of the cerebral blood flow (CBF) response to hypoxia the authors applied sinusoidally forced oscillations in O2 tension of inspired gas, at multiple frequencies, in the range of 0.001-0.05 Hz, to three anesthetized paralyzed goats. CBF was continuously measured by electromagnetic flowmeter and O2 saturation of arterial blood (SaO2) was continuously measured by means of a cuvette oximeter. The time series data relating CBF to SaO2, at each frequency were transformed by Fourier analysis and used in the construction of Bode plots by means of least-squares analysis. The data were satisfactorily fitted by a first-order transfer function. The average SaO2 values for the three animals were 84.6 ± 0.7, 59.3 ± 2.3, and 44.3 ± 0.9%. These were associated with corresponding dynamic sensitivity constants of 16.53, 16.17, and 11.93 (ml/min)/%sat and time constants of 35.7, 40.0, and 31.3 sec, respectively. Consideration of these time constants in the light of previous data suggests that the rate-limiting function for the CBF response to hypoxia is a process that is slower than simple diffusion of O2 to vascular smooth muscle. In addition, interdependent control systems, such as that involved in the ventilatory response to hypoxia, may be expected to manifest a dynamic component with a time constant in this range.