An implantable device (10) for the treatment of hydrocephalus, having a mechanical passive valve device or assembly (VAL) comprising a cylindrical body (CIL, 12); a piston (PIS, 13), housed slidingly (f1) in the cylindrical body (CIL); and a spring (MOL-NL, 17), having non-linear characteristic for applying a force on the piston (PIS) such that, when the overall pressure of the cerebrospinal fluid (CSF) exceeds, during the phase of cardiac systole, a certain value, a rapid displacement of the piston (PIS, 13) in the cylindrical body in one direction (f2) takes place and, when the pressure of the CSF falls below a certain value, during the phase of cardiac diastole, the piston (PIS), under the control of the non-linear spring (MOL-NL), reacts and moves rapidly in a direction opposite (f3) to the first, so as to feed once again into the ventricle (VEN) the CSF previously aspirated.