To assess the progress in myelination in the developing human brain, a prospective longitudinal study of flash visual evoked potentials (VEPs) was performed in 22 healthy preterm infants with the same gestational age at birth (between 30 weeks 0 day and 31 weeks 0 day). The individual curves of the changes in the N1a peak latency (the early peak of the N1 wave) decrease not linearly but in a stepwise pattern in the preterm period. Twenty-one infants out of the 22 have one or more 'acceleration week(s)' in which the latency decreases at a rate of more than 6 ms per week. These stepwise decreases in the latency may reflect a synchronized progress in myelination in several parts of the visual pathway. A detailed analysis of the 'acceleration weeks' in relation to postmenstrual age (PMA) indicates that they most prominently occur at 37 weeks PMA. At 37 weeks an initiation of myelination in the optic radiation has been demonstrated in post-mortem studies. We propose that a longitudinal follow-up study of VEPs can be accepted as a functional in vivo evaluation of myelination in the developing human brain.