Preterm infants often suffer from apnea of prematurity (AOP; a cessation of breathing) due to immaturity of the respiratory system. AOP can lead to oxygen shortage and a low heart rate which might harm the development of the newborn, especially the central nervous system. In order to prevent oxygen shortage, infants are treated with non-invasive respiratory support and caffeine. Despite these treatments, many preterm newborns still suffer from AOP and need invasive mechanical ventilation. Although this will result in complete resolution of AOP, invasive mechanical ventilation has the disadvantage of being a major risk of chronic lung disease and impaired neurodevelopmental outcome. Restrictive invasive ventilation is therefore advocated nowadays in preterm infants. Doxapram is a respiratory stimulant that has been administered off-label to treat AOP. Doxapram, as add-on treatment, seems to be effective in treating AOP and to prevent invasive mechanical ventilation. It is unclear if a preterm infant benefit from doxapram treatment on the longer term. This study compares doxapram to placebo and hypothesizes that doxapram will protect preterm infants from both invasive ventilation (and related lung disease) and AOP related oxygen shortage (and related impaired brain development).