Exhaust purification system of internal combustion engine

An exhaust purification system of an internal combustion engine wherein an exhaust purification catalyst for reacting NOx contained in exhaust gas and reformed hydrocarbons is arranged inside of an engine exhaust passage, aqueous urea solution feeding means and an NOx selective reduction catalyst able to reduce NOx by ammonia derived from an aqueous urea solution fed are arranged inside of the engine exhaust passage downstream of the exhaust purification catalyst, a precious metal catalyst is carried on an exhaust gas flow surface of the exhaust purification catalyst and a basic exhaust gas flow surface part is formed amount the previous metal catalyst, the exhaust purification catalyst has a property of reducing the NOx which is contained in exhaust gas if a concentration of hydrocarbons flowing into the exhaust purification catalyst is made to vibrate by within a predetermined range of amplitude and within a predetermined range of period and has a property of being increased in storage amount of NOx which is contained in exhaust gas if the vibration period of the hydrocarbon concentration is made longer than the predetermined range, and, at the time of engine operation, either method of a first NOx purification method which makes the concentration of hydrocarbons flowing into the exhaust purification catalyst vibrate by within the predetermined range of amplitude and within the predetermined range of period so as to reduce the NOx which is contained in exhaust gas in the exhaust purification catalyst and a second NOx purification method which uses the ammonia derived from the fed aqueous urea solution to reduce the NOx which is contained in exhaust gas at the NOx selective reduction catalyst is selectively used.