Surgically implantable device (10, 10-1, 10-2, 10-3, 10-4) for the treatment of hydrocephalus syndrome in a patient, comprising a mechanical passive valve device (VAL, 11-1, 11-2, 11-3, 11-4) designed to move and displace the cerebrospinal fluid or liquor in the cranial site of the patient in order to control the value of the actual intracranial pressure of said cerebrospinal fluid or liquor in said cranial site, the valve device comprising: - an outer cylindrical body (CIL, 12) having a substantially cylindrical shape; - a piston (PIS, 13) slidably arranged in said cylindrical body so as to define within it two distinct chambers (CAM-1, CAM-2, 14a-14b) separated by said piston, a first chamber (CAM-1, 14a), frontal, of said two chambers being designed to communicate, via a catheter, with a ventricle of the cranial site, whereby the sliding piston receives, on a respective face adjacent to said first chamber, the pressure of the cerebrospinal fluid contained in the ventricle; - a capillary tube (CAP, 16) for enabling communication between said two chambers (CAM-1,CAM-2, 14a-14b) and thereby allowing the cerebrospinal fluid to flow between them, and - a non-linear spring (MOL-NL, MOL-1, 17) associated in said cylindrical body (CIL, 12) with said piston (PIS, 13) in order to control its position, wherein said non-linear spring (MOL-NL, MOL-1, 17) has a special non-linear elastic characteristic (C') defining a first zone, with positive gradient, starting from a rest position, in which an increase in elongation of the spring (MOL-NL, MOL1, 17) corresponds to an increase in the force applied thereon; a successive second intermediate region, with negative gradient, in which instead an increase in elongation of the spring (MOL-NL, MOL-1, 17) corresponds to a decrease in the force applied; and finally a successive third zone, again with positive gradient, whereby the intermediate region of said non-linear characteristic of the spring (MOL-NL, MOL-1, 17) is a region in which the respective points are associated with a condition of instable equilibrium of the same spring (MOL-NL, MOL-1, 17), and consequently said spring (MOL-NL, MOL-1, 17) having said special non-linear elastic characteristic (C') is designed to apply, on said piston (PIS, 13), slidable, a corresponding elastic force such that, when the difference between the pressures applied by the cerebrospinal fluid on the two opposite faces of the piston (PIS, 13) is null, the piston is held in a rest position by said spring (MOL-1, 17) having said non-linear elastic characteristic; when the difference of the pressures applied by the cerebrospinal fluid on the two opposite faces of the piston (PIS, 13) exceeds, during the phase of cardiac systole, a certain predetermined value set in the calibration phase of the mechanical valve device (VAL, 11-1, 11-2, 11-3, 11-4), the piston (PIS, 13), due to the effect of said non-linear characteristic of the spring (MOL-NL, MOL-1, 17), moves rapidly in the cylindrical body (CIL, 12) towards the second chamber (CAM-2, 14b), rear, of said two chambers, resulting in a higher suction, by the same piston (PIS, 13), of the cerebrospinal fluid contained in the ventricle, and, when the intracranial pressure falls below a certain value, during the phase of cardiac diastole, the piston (PIS, 13), under the action and control of said non-linear spring (MOL-NL, MOL-1, 17), quickly returns back to the initial rest position, in order to infuse and re-enter in the cranial site the cerebrospinal fluid previously aspirated, so as to reduce, during the systolic phase, and to increase, during the diastolic phase, the value of the actual intracranial pressure in the ventricle, and thereby obtain, on the whole, a significant reduction or levelling of the intraventricular pulsatility, or of the change of the intracranial pressure in the ventricle, compared to the change that would occur in normal conditions in the absence of the device of the invention, while maintaining substantially unchanged and constant the average value of the intracranial pressure. - an outer cylindrical body (CIL, 12) having a substantially cylindrical shape; - a piston (PIS, 13) slidably arranged in said cylindrical body so as to define within it two distinct chambers (CAM-1, CAM-2, 14a-14b) separated by said piston, a first chamber (CAM-1, 14a), frontal, of said two chambers being designed to communicate, via a catheter, with a ventricle of the cranial site, whereby the sliding piston receives, on a respective face adjacent to said first chamber, the pressure of the cerebrospinal fluid contained in the ventricle; - a capillary tube (CAP, 16) for enabling communication between said two chambers (CAM-1,CAM-2, 14a-14b) and thereby allowing the cerebrospinal fluid to flow between them, and - a non-linear spring (MOL-NL, MOL-1, 17) associated in said cylindrical body (CIL, 12) with said piston (PIS, 13) in order to control its position,