An evaporative fuel-processing system for an internal combustion engine includes an evaporative emission control system having a canister for adsorbing evaporative fuel generated in the fuel tank, a passage extending between the fuel tank and the canister, a pressure-regulating valve arranged across the passage, for regulating pressure within the fuel tank to a predetermined value, and a pressure sensor for detecting pressure within the fuel tank. It is determined whether or not the evaporative emission control system is abnormal, based on the detected pressure within the fuel tank over a predetermined time period after starting of the engine. The predetermined time period is changed based on a parameter representative of the temperature of the fuel tank assumed at starting of the engine.