1. A braking device of the tilting system of a vehicle with more than two wheels, said vehicle having at least two wheels which tilt by means of said tilting system, the tilting system comprising at least a first hydraulic cylinder and a second hydraulic cylinder, each associated with a respective tilting wheel of the vehicle, said first and second hydraulic cylinder comprising a first and a second upper chamber containing oil, respectively, said first and second chamber being hydraulically connected to each other by a connection pipe, said braking device comprising braking means adapted to selectively either prevent or allow the oil flow in said hydraulic connection means and at least one central control unit and one or more detection devices, said central control unit being connected to said braking means and configured to receive and process one or more signals coming from said detection devices and to selectively actuate said braking means, wherein said braking means comprises a damper with an end part hydraulically connected to said connection pipe and a rotary piston present in the damper, said braking means additionally comprising at least two solenoid valves set on said hydraulic connection means, with at least one of said solenoid valves being set between said damper and the first hydraulic cylinder and at least one of said solenoid valves being set between said damper and said second hydraulic cylinder.