A method for measuring the cerebral perfusion of a living organism (1) by means of magnetic resonance (=“MR”) imaging proposes acquisition of further MR signals in a slice (5) that is pervaded by an artery that supplies the blood to the brain in order to determine the temporal progression of the concentration of the contrast medium during the bolus passage in the artery. During acquisition of the further MR signals, a magnetic field gradient is applied in such a way that projection images of the slice are generated. In each time interval between the excitations of the further MR signals, at least one radio-frequency (=“RF”) pulse is irradiated that causes saturation of the nuclear spin magnetization in the slice. This enables simultaneous measurement of the contrast medium flow in the vessels supplying the brain and the brain tissue within the same sequence with an adapted dynamic range.