A secondary air supplying apparatus of the present invention comprises a secondary air supplying device for supplying secondary air to upstream of an emission purifying device in an exhaust system of an internal combustion engine, a coolant temperature sensor for detecting a temperature of a coolant for the engine, an intake air temperature sensor for detecting a temperature of intake air, a supply controller for actuating the secondary air supplying device in accordance with a predetermined secondary air supply condition, and a summing unit for summing an actuation period of the secondary air supplying device and storing a sum. The supply controller stops the secondary air supply by the secondary air supplying device when the sum stored by the summing unit reaches a predetermined upper limit. The summing unit resets the stored sum, if a difference between the coolant temperature and the intake air temperature at a point before the actuation of the secondary air supplying device is not more than a predetermined value. This configuration enables the apparatus to suppress oversupply of secondary air and overheating of a catalyst so as to implement appropriate activation of the catalyst.