1. An air-fuel ratio control system for an internal combustion engine, for controlling an air-fuel ratio of a mixture supplied to the engine, comprising: combustion state parameter-detecting means for detecting a combustion state parameter indicative of a combustion state of the mixture in the engine; operating state parameter-detecting means for detecting an operating state parameter indicative of an operating state of the engine; exhaust gas state parameter-estimating means for estimating an exhaust gas state parameter indicative of a state of exhaust gases emitted from the engine, as an estimated exhaust gas state parameter, by inputting the detected combustion state parameter and the detected operating state parameter to a neural network configured as a neural network to which are input the combustion state parameter and the operating state parameter, and in which the exhaust gas state parameter is used as a teacher signal; and air-fuel ratio control means for controlling the air-fuel ratio based on the estimated exhaust gas state parameter.