A wheel (1) of a railway vehicle is associated with a vibration sensor (3) for supplying a vibration impulsive signal (V), indicative of the vibration of the wheel, to an electronic processing unit (E). This generates, based on the vibration signal (V), an impulsive surveillance signal (S) the instant value of which is increased in a manner correlated to the amplitude of each vibration impulse (I) and decreased in accordance with a predetermined law after each vibration impulse. The processing unit (E) compares the instant value of the surveillance signal (S) with a reference threshold value (T) and automatically generates an alarm signal (A) when the instant value of the surveillance signal (S) reaches or exceeds the reference threshold value (T).
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