An exhaust gas control apparatus comprising: an exhaust gas control member that is provided in an exhaust system of an internal combustion engine in order to control an exhaust gas by removing a predetermined component contained in the exhaust gas; a purifying agent supply device that supplies a purifying agent to an upstream side of the exhaust gas control member in the exhaust system so that the purifying agent is adsorbed to the exhaust gas control member and caused to react with the predetermined component in the exhaust gas that passes through the exhaust gas control member; a control device that obtains a purifying agent adsorption amount distribution through the exhaust gas control member and controls a purifying agent supply supplied by the purifying agent supply device on the basis of the obtained purifying agent adsorption amount distribution; wherein on a model obtained by dividing the exhaust gas control member into a plurality of cells in the exhaust gas flow direction, the control device obtains the purifying agent adsorption amount distribution through the exhaust gas control member on the basis of a detected value and/or an estimated value of a purifying agent adsorption amount in each cell, the purifying agent adsorption amount corresponds to an adsorption amount of the purifying agent supplied by the purifying agent supply device; characterised in that the control device obtains a slip determination value, which is an index for determining a likelihood that the purifying agent flows out of the exhaust gas control member, on the basis of the purifying agent adsorption amount distribution through the exhaust gas control member, and when the slip determination value equals or exceeds a predetermined second threshold, controls the purifying agent supply device to stop the purifying agent supply or reduce a purifying agent supply amount. an exhaust gas control member that is provided in an exhaust system of an internal combustion engine in order to control an exhaust gas by removing a predetermined component contained in the exhaust gas; a purifying agent supply device that supplies a purifying agent to an upstream side of the exhaust gas control member in the exhaust system so that the purifying agent is adsorbed to the exhaust gas control member and caused to react with the predetermined component in the exhaust gas that passes through the exhaust gas control member; a control device that obtains a purifying agent adsorption amount distribution through the exhaust gas control member and controls a purifying agent supply supplied by the purifying agent supply device on the basis of the obtained purifying agent adsorption amount distribution; wherein on a model obtained by dividing the exhaust gas control member into a plurality of cells in the exhaust gas flow direction, the control device obtains the purifying agent adsorption amount distribution through the exhaust gas control member on the basis of a detected value and/or an estimated value of a purifying agent adsorption amount in each cell, the purifying agent adsorption amount corresponds to an adsorption amount of the purifying agent supplied by the purifying agent supply device; characterised in that the control device obtains a slip determination value, which is an index for determining a likelihood that the purifying agent flows out of the exhaust gas control member, on the basis of the purifying agent adsorption amount distribution through the exhaust gas control member, and when the slip determination value equals or exceeds a predetermined second threshold, controls the purifying agent supply device to stop the purifying agent supply or reduce a purifying agent supply amount.