The inventive system comprises means (10) for determining the vehicle running mode, means (11) for determining the mass of elementary carbon exhausted by the engine according said running mode, means (15) for accumulating said elementary masses during the engine operation and obtaining a total mass thereof, means (18) for calculating the volume of ash from engine lubrication oil, means (20) for calculating the volume of ash from engine feed fuel, means (21) for calculating the effective volume of the depollution means on the basis of the total volume of the means thereof as they are new or cleaned, the already calculated volume of ash and means for calculating the degree of soot loading of the depollution means on the basis of the total mass, the effective volume and the maximum density of deposits on the depollution means.