It is of principal worry the neurological sequels in the extreme premature babies. These can go from severe alterations up to minimal disorders. The managing of the critical patient includes the strict and continuous monitoring of the vital signs. The cerebral function is of evaluation limited in the acute period of these patients. The electroencephalography is the expression of the membrane potential in rest neuronal. One has seen that the changes in cerebral flow affect the electrical sign emitted by this one. There have been reported that some conditions that in the neonatal period are associated with alterations of cerebral flow. This way there is described, that the application of surfactant is associated with fluctuations of the cerebral flow, the arterial unbalanced ductus, Indomethacin's injection in less than 30 minutes, episodes of severe hypoxemia , Methylxanthines's injection,etc.