Neonatal hyperinsulinemic hypoglycemia must be suddenly and appropriately diagnosed and treated to prevent any further neurological dysfunction and damage. Therefore, we report two cases of our observation. Case 1: birth asphyxia, episodes of hypoglycemia after delivery, hyperinsulinism and reduced IGFBP1 blood concentration. Clinical and laboratory pictures resolved progressively after 8 days of life, perfusions were stopped and the neonate began to suck breast milk. Case 2: negative familial and perinatal history. On the 3rd day of life he developed cyanosis, hypotonia, tremors and hypoglycemia. He was discharged with a diagnosis of cerebral injury and neonatal hypoglycemia. At 1 year of life the child showed progressive and heavy neurological damage. The RMN of the brain showed: enlarged ventricles and liquor spaces around the brain, particularly in the frontal region. Hyperinsulinism was diagnosed in our Clinic. He began pharmacological treatment with Diazoxide that permitted euglycemia. The ammonium was normal and excluded glutamate dehydrogenase deficiency (mutation of GLUD1 gene); Diazoxide responsivity excluded mutations of SUR1 and KIR6.3 genes. At 9 years of life he showed motor and language retardation. Newborns with perinatal history of asphyxia may develop transient hyperinsulinism with absent neurological consequences. Persistent hypoglycemic or epileptic-like episodes, in particular on waking up, after meals or during banal infections, must be studied to reveal hyperinsulinism.