An anti-derailment system is described for a wheel which can roll on a track and is pivoted on a carriage which translatably supports a leaf of a piece of furniture. The system has a slider which is inseparably mountable or mounted on the track and is able to translate on the track independently of the carriage, and a constraint element for constraining the slider and at least one of the wheel, the carriage or the leaf to each other, so as to keep the wheel in condition of rolling on the track without derailing.