An apparatus for the prevention and damping of voltage and current peaks of internal and external origin with respect to power lines preferably at medium, high and very-high voltage, based on the detection and transformation of electromagnetic energy causing the overvoltages and overcurrents comprising: at least one functional unit, in use, connected between a conductor of a power line and an earthing system as described below, wherein said functional unit comprises in turn: - a tuning device comprising a pair of electrodes, of which one input, in use, connected to a phase of the power line for receiving an electrical signal, and one output; said tuning device being configured to realise a passage of said electrical signal between the two electrodes, only when said electrical signal has a frequency exceeding a predetermined threshold; - a damping device connected to said output electrode of the tuning device and configured to dissipate the energy load of said electrical signal; wherein an input electrode of said damping device is coupled to said output electrode of the tuning device through a harmonising device, while an output electrode of the damping device 4, in use, is earth polarised by means of connection to the earthing system; wherein said damping device has an electrically isolated internal volume with respect to the external of the damping device itself and comprising a mixture of an incoherent, non-hygroscopic sediment of particles of a piezoelectric, pyroelectric and refractory inert material; said damping device comprising and having a metallic heat interception bar partly immersed in said mixture, coupled to a heat dissipation collar made of metal which realises a radiator, and adapted to disperse the heat produced by said energy load towards the outside of the damping device itself so that said functional unit is configured to absorb, dampen and dissipate the energy load of said electrical signal at the origin of the voltage and current pulses with a steep front so as to achieve the prevention of the formation of said voltage and current peaks; characterised in that the harmonising device interposed between the tuning device and the damping device is configured to realise a capacitive coupling therebetween; said harmonising device comprising a coiled conductor wound on a dielectric cylindrical support. at least one functional unit, in use, connected between a conductor of a power line and an earthing system as described below, wherein said functional unit comprises in turn: - a tuning device comprising a pair of electrodes, of which one input, in use, connected to a phase of the power line for receiving an electrical signal, and one output; said tuning device being configured to realise a passage of said electrical signal between the two electrodes, only when said electrical signal has a frequency exceeding a predetermined threshold; - a damping device connected to said output electrode of the tuning device and configured to dissipate the energy load of said electrical signal; wherein an input electrode of said damping device is coupled to said output electrode of the tuning device through a harmonising device, while an output electrode of the damping device 4, in use, is earth polarised by means of connection to the earthing system; - a tuning device comprising a pair of electrodes, of which one input, in use, connected to a phase of the power line for receiving an electrical signal, and one output; said tuning device being configured to realise a passage of said electrical signal between the two electrodes, only when said electrical signal has a frequency exceeding a predetermined threshold; - a damping device connected to said output electrode of the tuning device and configured to dissipate the energy load of said electrical signal; wherein an input electrode of said damping device is coupled to said output electrode of the tuning device through a harmonising device, while an output electrode of the damping device 4, in use, is earth polarised by means of connection to the earthing system; wherein said damping device has an electrically isolated internal volume with respect to the external of the damping device itself and comprising a mixture of an incoherent, non-hygroscopic sediment of particles of a piezoelectric, pyroelectric and refractory inert material; said damping device comprising and having a metallic heat interception bar partly immersed in said mixture, coupled to a heat dissipation collar made of metal which realises a radiator, and adapted to disperse the heat produced by said energy load towards the outside of the damping device itself so that said functional unit is configured to absorb, dampen and dissipate the energy load of said electrical signal at the origin of the voltage and current pulses with a steep front so as to achieve the prevention of the formation of said voltage and current peaks; characterised in that the harmonising device interposed between the tuning device and the damping device is configured to realise a capacitive coupling therebetween; said harmonising device comprising a coiled conductor wound on a dielectric cylindrical support.