A device for disconnecting the feed of fuel to an internal combustion engine with an injection pump during the coasting of an automotive vehicle comprises a solenoid valve for disconnecting and reconnecting the feed of the fuel. The valve is controlled by the decrease in the speed of the internal combustion engine. In order to adapt the disconnect threshold and the reconnect threshold of the feed of the fuel to the characteristic curve of the internal combustion engine at little expense but nevertheless with a large saving in fuel, the solenoid valve is connected to an outlet line of an idle-speed controller which is provided for the same internal combustion engine. The time response of the controller has at least a differential portion in addition to a proportional portion, but possibly proportional, integral and differential portions. The adaptation of the time response portions to the dynamic behavior of the internal combustion engine is the same as for the control for the idling speed.