Abstract : Although the study of cerebral vasoreactivity using fMRI is mainly conducted through the BOLD fMRI modality, owing to its relatively high signal-to-noise ratio (SNR), ASL fMRI provides a more interpretable measure of cerebral vasoreactivity than BOLD fMRI. Still, ASL suffers from a low SNR and is hampered by a large amount of physiological noise. The current contribution aims at improving the re- covery of the vasoreactive component from the ASL signal. To this end, a Bayesian hierarchical model is proposed, enabling the recovery of per- fusion levels as well as fitting their dynamics. On a single-subject ASL real data set involving perfusion changes induced by hypercapnia, the approach is compared with a classical GLM-based analysis. A better goodness-of-fit is achieved, especially in the transitions between baseline and hypercapnia periods. Also, perfusion levels are recovered with higher sensitivity and show a better contrast between gray- and white matter.