A device for preventing overfilling of containers, such as those intended to contain liquefied gases, includes a valve body in which a gas duct is defined and a closure. The closure is axially movable in the valve body away from and towards a valve seat in order to respectively open and shut off the gas duct. An actuator, capable of exerting a thrust, urges the closure away from the seat. The actuator includes a float, a cam mechanism and a lever mechanism. The cam mechanism exerts the thrust in an ascending phase of the float until a preimposed limit position corresponding to a maximum filling level is reached. The lever mechanism exerts the thrust in at least a first part of a descending phase of the float starting from the limit position.