A system for detecting the speed of an engine for a vehicle calculates the engine speed in accordance with a signal which is outputted from a main rotation sensor in accordance with the operation of the engine. In case the main rotation sensor is subjected to malfunction, the engine speed is calculated using a back-up signal. Namely, an auxiliary rotation sensor detects the rotation of a portion of a power transmission device. When the above portion of the power transmission device is connected to an output shaft of the engine, the signal from the auxiliary rotation sensor is used as the back-up signal. When the two are disconnected from each other, a signal, representing the condition of the operation of an actuator for controlling the amount of supply of fuel to the engine, is used as the back-up signal.