An exhaust gas-purifying system that purifies exhaust gas emitted by a combustion engine mounted on an automotive vehicle, comprising: an exhaust gas-purifying unit that includes one or more exhaust gas-purifying catalysts (712, 722), is supplied with the exhaust gas from the combustion engine, and purifies the exhaust gas so that the exhaust gas can be released to the atmosphere; an air flow meter; a speedometer or distance meter; a sensor that detects a concentration of nitrogen oxides contained in the exhaust gas purified by the exhaust gas-purifying unit; and a processing section that makes a judgment with respect to at least one of the one or more exhaust gas-purifying catalysts (712, 722), as to whether or not a performance is maintained at a sufficient level, based on the concentration detected by the sensor, characterized in that the processing section calculates for each of two or more time intervals, an amount of nitrogen oxides emitted by the automobile vehicle per unit driving distance from the concentration detected by the sensor within the time interval, an amount or a flow rate of air supplied to the combustion engine detected by the air flow meter within the time interval, and a driving distance or a driving velocity of the automotive vehicle detected by the speedometer or the distance meter within the time interval, to determine a relationship between an amount of nitrogen oxides emitted by the automobile vehicle per unit driving distance and a driving distance, estimates a cumulative driving distance at which the amount of nitrogen oxides emitted by the automotive vehicle per unit driving distance reaches a third set value, by extrapolation from the relationship, and the processing section makes a judgment with respect to the at least one of the one or more exhaust gas-purifying catalysts (712, 722) that a replacement is necessary or a replacement time is approaching, if a difference between the estimated cumulative driving distance and an actual cumulative driving distance is less than a fourth set value or is less than or equal to the fourth set value. an exhaust gas-purifying unit that includes one or more exhaust gas-purifying catalysts (712, 722), is supplied with the exhaust gas from the combustion engine, and purifies the exhaust gas so that the exhaust gas can be released to the atmosphere; an air flow meter; a speedometer or distance meter; a sensor that detects a concentration of nitrogen oxides contained in the exhaust gas purified by the exhaust gas-purifying unit; and a processing section that makes a judgment with respect to at least one of the one or more exhaust gas-purifying catalysts (712, 722), as to whether or not a performance is maintained at a sufficient level, based on the concentration detected by the sensor, characterized in that the processing section calculates for each of two or more time intervals, an amount of nitrogen oxides emitted by the automobile vehicle per unit driving distance from the concentration detected by the sensor within the time interval, an amount or a flow rate of air supplied to the combustion engine detected by the air flow meter within the time interval, and a driving distance or a driving velocity of the automotive vehicle detected by the speedometer or the distance meter within the time interval, to determine a relationship between an amount of nitrogen oxides emitted by the automobile vehicle per unit driving distance and a driving distance, estimates a cumulative driving distance at which the amount of nitrogen oxides emitted by the automotive vehicle per unit driving distance reaches a third set value, by extrapolation from the relationship, and the processing section makes a judgment with respect to the at least one of the one or more exhaust gas-purifying catalysts (712, 722) that a replacement is necessary or a replacement time is approaching, if a difference between the estimated cumulative driving distance and an actual cumulative driving distance is less than a fourth set value or is less than or equal to the fourth set value.