An evaporating fuel processing apparatus of an internal combustion engine is disclosed, which can reliably determine the presence or absence of leakage even if stopping and restarting operations of the internal combustion engine are alternately repeated. The apparatus comprises a leakage detecting section for detecting leakage in the evaporating fuel processing apparatus by referring to parameters; a stop condition determining section for determining whether a predetermined condition for stopping the internal combustion engine is satisfied; a stop section for stopping the internal combustion engine when the stop condition determining section determines that the predetermined condition is satisfied; a restart section for restarting the internal combustion engine after the internal combustion engine is stopped by the stop section; a storage section for storing parameters referred to by the leakage detecting section; and an initializing section for initializing the parameters when an ignition switch for starting the internal combustion engine is switched on.