Understanding the rapid evolution of cerebral cortical surfaces in developing neonates is essential in order to understand normal human brain development and to study anatomical abnormalities in preterm infants. Several methods to model and align cortical surfaces for cross-sectional studies have been developed. However, the registration of cortical surfaces extracted from neonates across different gestational ages for longitudinal studies remains difficult because of significant cerebral growth. In this paper, we present an automatic cortex registration algorithm, based on surface relaxation followed by non-rigid surface registration. This technique aims to establish the longitudinal spatial correspondence of cerebral cortices for the developing brain in neonates. The algorithm has been tested on 5 neonates. Each infant has been scanned at three different time points. Quantitative results are obtained by propagating sulci across multiple gestational ages and computing the overlap ratios with manually established ground-truth.