An engine control apparatus is applied to a system including rotating electrical machine, a battery connected to the rotating electrical machine via a power conversion circuit, and an electric load. The engine control apparatus determines that engine speed is within a predetermined rotation speed range including at least a resonance range of an engine during a rotation drop period while engine speed drops to zero after engine combustion is stopped, and, in the case where it is determined that engine speed is within predetermined rotation speed range, selectively performs one of first rotation drop processing of increasing reduction rate of engine speed by regenerative power generation of the rotating electrical machine and second rotation drop processing of increasing reduction rate of engine speed by causing rotating electrical machine to perform power driving on an inverse rotation side. At a rotation drop control unit the first rotation drop processing is performed.