An exhaust gas purification apparatus for an internal combustion engine and for use with: (a) a selective catalytic reduction NOx catalyst having a catalyst substrate and a plurality of catalyst layers made up of catalyst particles having the property of selectively reducing NOx with a reducing agent derived from ammonia arranged on the catalyst substrate, the catalyst layers including at least a high-temperature catalyst layer having high capability of reducing NOx at high temperatures and a low-temperature catalyst layer having higher capability of reducing NOx at low temperatures than that of said high-temperature catalyst layer and arranged closer to said catalyst substrate than said high-temperature catalyst layer; and (b) an addition means for adding, to exhaust gas flowing into said selective catalytic reduction NOx catalyst, a determined addition quantity of reducing agent for reducing NOx; the exhaust gas purification apparatus comprising: control means that is configured to control addition of the reducing agent by said addition means during a reducing agent addition period from the time at which said determined addition quantity of reducing agent is added by said addition means to the time at which said determined addition quantity of reducing agent is added by said addition means at the subsequent reducing agent addition period; wherein the control means is configured to control the addition means, when the temperature of said selective catalytic reduction NOx catalyst is in a predetermined low temperature range in which the NOx reducing capability of said low-temperature catalyst layer is higher than the NOx reducing capability of said high-temperature catalyst layer, to control the concentration of the reducing agent in a reducing agent atmosphere formed in the exhaust gas flowing into said selective catalytic reduction NOx catalyst to be higher than when the temperature of said selective catalytic reduction NOx catalyst is in a predetermined high temperature range that is higher than said predetermined low temperature range and in which the NOx reducing capability of said high-temperature catalyst layer is higher than the NOx reducing capability of said low-temperature catalyst layer, provided that said predetermined addition quantity is the same; wherein as said predetermined addition quantity of reducing agent is added to the exhaust gas by said addition means, the reducing agent concentration in said reducing agent atmosphere changes with time, and characterized in that: said control means is configured to control addition of the reducing agent by said addition means to control the difference between the highest value and the lowest value of the reducing agent concentration in said reducing agent atmosphere during said reducing agent addition period when the temperature of said selective catalytic reduction NOx catalyst is in said predetermined low temperature range to be larger than the difference between the highest value and the lowest value of the reducing agent concentration in said reducing agent atmosphere when the temperature of said selective catalytic reduction NOx catalyst is in said predetermined high temperature range. control means that is configured to control addition of the reducing agent by said addition means during a reducing agent addition period from the time at which said determined addition quantity of reducing agent is added by said addition means to the time at which said determined addition quantity of reducing agent is added by said addition means at the subsequent reducing agent addition period; wherein the control means is configured to control the addition means, when the temperature of said selective catalytic reduction NOx catalyst is in a predetermined low temperature range in which the NOx reducing capability of said low-temperature catalyst layer is higher than the NOx reducing capability of said high-temperature catalyst layer, to control the concentration of the reducing agent in a reducing agent atmosphere formed in the exhaust gas flowing into said selective catalytic reduction NOx catalyst to be higher than when the temperature of said selective catalytic reduction NOx catalyst is in a predetermined high temperature range that is higher than said predetermined low temperature range and in which the NOx reducing capability of said high-temperature catalyst layer is higher than the NOx reducing capability of said low-temperature catalyst layer, provided that said predetermined addition quantity is the same; wherein as said predetermined addition quantity of reducing agent is added to the exhaust gas by said addition means, the reducing agent concentration in said reducing agent atmosphere changes with time, and characterized in that: said control means is configured to control addition of the reducing agent by said addition means to control the difference between the highest value and the lowest value of the reducing agent concentration in said reducing agent atmosphere during said reducing agent addition period when the temperature of said selective catalytic reduction NOx catalyst is in said predetermined low temperature range to be larger than the difference between the highest value and the lowest value of the reducing agent concentration in said reducing agent atmosphere when the temperature of said selective catalytic reduction NOx catalyst is in said predetermined high temperature range.