The aim of this study was to follow the evolution of neurological findings in a cohort of near-term infants born between 35 and 37 weeks. A total of 448 infants born between 35 and 36.9 weeks gestational age with normal cranial ultrasonograms or only minor abnormalities, were studied using the Hammersmith Infant Neurological Examination, at 6, 9 and 12 months (corrected for prematurity). Our results showed that while some items such as cranial nerve and movements showed minimal changes over time, other items mainly related to "tone", "posture" and "reflexes" showed progressive maturation. There was no significant difference between the infants born at 35 and 36 weeks gestation. When compared to term infants assessed at the same age intervals, our cohort showed a wider variability of scores. Mean and 10 (th) percentile for global scores were lower than those reported for term infants suggesting that when assessing infants born at 35 and 36 weeks the optimality scores used for infants born full-term should not be used as normative data. Our results, providing longitudinal data in near-term infants without brain lesions, can be used as a reference in both clinical and research setting to monitor early neurological signs in those children.