Disclosed herein are methods of treating retinopathy of prematurity (ROP) in a premature and/or low birth weight infant in need thereof, comprising administering to the infant an effective amount of a compound represented by Structural Formula I, Structural Formula Ia or Structural Formula II described herein, or a pharmaceutically acceptable salt thereof. Also disclosed herein are methods of inhibiting the destruction of retinal blood vessels in a premature and/or low birth weight infant in need thereof, comprising administering to the infant an effective amount of a compound represented by Structural Formula I, Structural Formula Ia or Structural Formula II, or a pharmaceutically acceptable salt thereof. Also disclosed herein are methods of treating hyperoxia in a premature and/or low birth weight infant in need thereof, comprising administering to the infant an effective amount of a compound represented by Structural Formula I, Structural Formula Ia or Structural Formula II, or a pharmaceutically acceptable salt thereof. By using the methods disclosed herein, particularly when an infant is hyperoxic, oxygen toxicity to the retina of the eye can be inhibited without restricting oxygen supplementation, which is often necessary to sustain the life of premature infants.