The present invention relates to a method and device for triggering an automatic emergency braking process in a vehicle to avoid a tail-end collision with an obstacle, wherein a warning to the driver is triggered if at least one warning condition is satisfied, wherein the satisfaction of the warning condition specifies that owing to the instantaneous driving situation of the vehicle relative to the obstacle the automatic emergency braking process should be triggered, wherein the automatic emergency braking process is not triggered until after the warning to the driver is triggered and a warning time period has subsequently expired, wherein the warning time period is set as a function of the relative movement situation between the vehicle and the obstacle and/or is adapted as a function of a relative movement, which changes over time, between the vehicle and the obstacle.