In many neuroscience applications, the Arterial Spin Labeling (ASL) fMRI modality arises as a preferable choice to the standard BOLD modality due to its ability to provide a quantitative measure of the Cerebral Blood Flow (CBF). Such a quantification is central but generally performed without consideration of a specific modeling of the perfusion component in the signal often handled via standard GLM approaches using the BOLD canonical response function as regressor. In this work, we propose a novel Bayesian hierarchical model of the ASL signal which allows activation detection and both the extraction of a perfusion and a hemodynamic component. Validation on synthetic and real data sets from event-related ASL show the ability of our model to address the source separation and double deconvolution problems inherent to ASL data analysis.