Sufficient O2-supply to the brain is necessary for an adequate cerebral energy metabolism, function and growth. To elucidate the relation between changes in, respectively, mean arterial blood pressure (MABP) and cerebral O2-supply and changes in the oxygenation state of hemoglobin during hypotension in preterm born lambs. Preterm lambs were delivered at 141 days (n=7) or 127 days (n=7) of gestation. Hypotension was induced by stepwise withdrawal of blood. Cerebral arterial blood gases were analyzed at the end of each level to calculate cerebral O2-supply. Near-infrared spectroscopy was used to measure changes in the concentration of cerebral oxyhemoglobin (cO2Hb), deoxyhemoglobin (cHHb) and cHbD (the difference between cO2Hb and cHHb). In the 141 and the 127 d lambs, changes in MABP and cerebral O2-supply were positively linearly related with $Δ$cO2Hb, and negatively with $Δ$cHHb. MABP was positively linearly related with changes in cHbD. During hemorrhagic hypotension, changes in MABP and cerebral O2-supply are reflected by changes in the oxygenation state of cerebral hemoglobin in near-term born lambs.