The risk of oxidative stress is high in preterm newborns. Room air exposure of an organism primed to develop in a hypoxic environment, lacking antioxidant defenses, and subjected to hyperoxia, hypoxia, and ischemia challenges the newborn with oxidative stress production. Free radicals can be generated by a multitude of other mechanisms, such as glutamate excitotoxicity, excess free iron, inflammation, and immune reactions. Free radical-induced damage caused by oxidative stress appears to be the major candidate for the pathogenesis of most of the complications of prematurity, brain being especially at risk, with short to long-term consequences. We review the role of free radical oxidative damage to the newborn brain and propose a mechanism of oxidative injury, taking into consideration the particular maturation-dependent vulnerability of the oligodendrocyte precursors. Prompted by our observation of an increase in plasma Adenosine concentrations significantly associated with brain white matter lesions in some premature infants, we discuss a possible bioenergetics hypothesis, correlated to the oxidative challenge of the premature infant. We aim at explaining both the oxidative stress generation and the mechanism promoting the myelination disturbances. Being white matter abnormalities among the most common lesions of prematurity, the use of Adenosine as a biomarker of brain damage appears promising in order to design neuroprotective strategies.