A control device for an engine, comprising: an air-fuel ratio detection unit that detects an air-fuel ratio of exhaust gas in an exhaust pipe; and an air-fuel ratio change unit that changes an air-fuel ratio of exhaust gas in the exhaust pipe in a predetermined cycle, a unit which sends a notification of an abnormality in the air-fuel ratio detection unit or causes at least a portion of engine control to run in a fail-safe mode when a dead time abnormality determination unit detects deterioration of dead time characteristics of the air-fuel ratio detection unit when an amplitude of an output signal of the air-fuel ratio detection unit at a predetermined frequency, while the air-fuel ratio is changed by the air-fuel ratio change unit, is equal to or more than a first predetermined value, and a required time or a required angle to arrive at a predetermined value of an output signal of the air-fuel ratio detection unit from a reference time point or a reference position of a parameter related to a phase of the engine is equal to or more than a second predetermined value, wherein a Fourier transform unit that performs a Fourier transform on the output signal of the air-fuel ratio detection unit; an amplitude calculation unit that obtains the amplitude from a power spectrum obtained through the Fourier transform; and a required time calculation unit that obtains the required time or the required angle to arrive the predetermined value of the output signal of the air-fuel ratio detection unit from a phase spectrum obtained through the Fourier transform and from the reference position or the reference time point of the engine-related parameter. an air-fuel ratio detection unit that detects an air-fuel ratio of exhaust gas in an exhaust pipe; and an air-fuel ratio change unit that changes an air-fuel ratio of exhaust gas in the exhaust pipe in a predetermined cycle, a unit which sends a notification of an abnormality in the air-fuel ratio detection unit or causes at least a portion of engine control to run in a fail-safe mode when a dead time abnormality determination unit detects deterioration of dead time characteristics of the air-fuel ratio detection unit when an amplitude of an output signal of the air-fuel ratio detection unit at a predetermined frequency, while the air-fuel ratio is changed by the air-fuel ratio change unit, is equal to or more than a first predetermined value, and a required time or a required angle to arrive at a predetermined value of an output signal of the air-fuel ratio detection unit from a reference time point or a reference position of a parameter related to a phase of the engine is equal to or more than a second predetermined value, wherein a Fourier transform unit that performs a Fourier transform on the output signal of the air-fuel ratio detection unit; an amplitude calculation unit that obtains the amplitude from a power spectrum obtained through the Fourier transform; and a required time calculation unit that obtains the required time or the required angle to arrive the predetermined value of the output signal of the air-fuel ratio detection unit from a phase spectrum obtained through the Fourier transform and from the reference position or the reference time point of the engine-related parameter.