The coherence function has been used in transfer function analysis of dynamic cerebral autoregulation to assess the statistical significance of spectral estimates of gain and phase frequency response. Interpretation of the coherence function and choice of confidence limits has not taken into account the intrinsic non-linearity represented by changes in cerebrovascular resistance due to vasomotor activity. For small spontaneous changes in arterial blood pressure (ABP), the relationship between ABP and cerebral blood flow velocity (CBFV) can be linearized, showing that corresponding changes in cerebrovascular resistance should be included as a second input variable. In this case, the standard univariate coherence function needs to be replaced by the multiple coherence, which takes into account the contribution of both inputs to explain CBFV variability. Using two different indicators of cerebrovascular resistance (CVRi = ABP/CBFV and the resistance-area product, RAP), multiple coherences were calculated for 42 healthy control subjects, aged from 20 to 40 years old (mean ± SD 28 ± 4.6 years), at rest in the supine position. CBFV was measured in both middle cerebral arteries and ABP was recorded non-invasively by finger photoplethysmography. Results for the ABP+RAP inputs show that the multiple coherence of CBFV for frequencies < 0.05 Hz is significantly higher than the corresponding values obtained for univariate coherence (p<10^-5). Corresponding results for the ABP+CVRi inputs confirm the principle of multiple coherence, but are less useful due to the interdependence between CVRi, ABP and CBFV. The main conclusion is that values of univariate coherence between ABP and CBFV should not be used to reject spectral estimates of gain and phase, derived from small fluctuations in ABP, since the true explained power of CBFV in healthy subjects is much higher than what has been usually predicted by the univariate coherence functions.