A control device including a reversing valve, disposed in fuel lines into which a feed pump is introduced between a fuel supply tank and a suction chamber of a fuel injection pump, by means of which valve, to turn off an internal combustion engine operated with the fuel injection pump, the line connections are variable in such a way that the suction chamber communicates with the intake side of the feed pump and the compression side of the feed pump communicates with the fuel supply tank. As its valve member, the reversing valve has a slide, which carries first and second double-seat-valve closing bodies that cooperate with corresponding valve seats. The first and second double-seat-valve closing bodies form sealing elements which are detachably buttoned onto the slide that are made of an elastically deformable material. The sealing elements are provided with elastically deformable sealing lips pointing to the valve seats, so that oppositely disposed valve seats of each seat are reliably sealed off even if there are dimensional variations from manufacturing tolerances.