It is shown theoretically that the flow-sensitive alternating inversion recovery (FAIR) signal intensity difference for flow quantification is independent of the length of the predelay between repeated measurements when assuming complete labeling in between scans. Theory also predicts that flows quantified using the concomitant T1 difference increase significantly with decreasing predelay, because the biexponential relaxation behavior after nonselective inversion is fitted as a monoexponential. The new equations include the effect of the unequal relaxation times of water in tissue (T1) and arterial blood (T1a). While this effect is significant for the signal-difference approach, it is negligible for the T1-difference procedure when using maximum inversion-recovery times shorter than 4 sec. Experiments on cat brain using the FAIR excluding radiation damping (FAIRER) pulse sequence at three different predelays (0.8, 2, and 5 sec) confirm the theoretical predictions.