Abstract: A method is described for indicating the dynamic instability of railway or tramway rolling stock. The method essentially consists in detecting, by means of at least one accelerometer sensor, the acceleration of the wheel arrangement of the rolling stock in a direction transverse the direction of travel, suitably processing it and subsequently comparing, in a suitable comparator, the processed acceleration value with a reference value v.sub.O. The indication of instability is obtained by checking whether the number of processed acceleration values which exceed the said reference value is greater than a predetermined number in a predetermined period of time.