Cerebrovascular autoregulation is evaluated from spontaneous fluctuations in mean flow velocity (MFV) by transcranial Doppler ultrasound of the middle cerebral artery (MCA) with respect to changes in arterial blood pressure (BP_MCA), but the effects of spontaneous fluctuations in arterial Pco ₂ on MFV have been largely ignored. Autoregressive moving average analysis (ARMA), a closed-loop system identification technique, was applied to data from nine healthy subjects during spontaneous breathing, during inspiration of 10% CO₂ for two breaths once per minute for 4 min, and during sustained breathing of 7% CO₂. Cerebrovascular resistance index (CVRi) was calculated (CVRi = BP_MCA/MFV). Reliable estimates of gain for BP_MCA → MFV were obtained for spontaneous breathing and the two-breath method. In contrast, reliable gain estimates for Pco ₂ → MFV or Pco ₂ → CVRi were achieved only under the two-breath method. Pco ₂ → MFV gain was smaller with the two-breath method than during sustained 7% CO₂ ( P < 0.05). BP_MCA was elevated by 7% CO₂ but not by the two-breath method. The closed-loop model provides insight into interactions between BP_MCA and Pco ₂ on cerebrovascular control, but reliable solutions for Pco ₂effects with ARMA analysis require perturbation by the two-breath method.