Background: Postpartum developmental delay has been proposed as an important phenotype of human evolution which contributes to many human-specific features including the increase in brain size and the advanced humanspecific cognitive traits. However, the biological processes and molecular functions underlying early brain development still remain poorly understood, especially in human and primates. Results: In this paper, we comparatively and extensively studied dorsolarteral prefrontal cortex expression data in human and chimpanzee to investigate the critical processes or biological events during early brain development at a molecular level. By using the dynamic network biomarker (DNB) model, we found that there are tipping points around 3 months and 1 month, which are crucial periods in infant human and chimpanzee brain development, respectively. In particular, we shown that the human postnatal development and the corresponding expression changes are delayed 3 times relative to chimpanzee, and we also revealed that many common biological processes are highly involved in those critical periods for both human and chimpanzee, e.g., physiological system development functions, nervous system development, organismal development and tissue morphology. These findings support that the maximal rates of brain growth will be in those two critical periods for respective human and primates. In addition, different from chimpanzee, our analytic results also showed that human can further develop a number of advanced behavior functions around this tipping point (around 3 months), such as the ability of learning and memory. Conclusion: This work not only provides biological insights into primate brain development at a molecular level but also opens a new way to study the criticality of nonlinear biological processes based on the observed omics data.