Method for initiating an automatic emergency braking process in a vehicle driving ahead of at least one following vehicle (60 to 120) in order to prevent the leading vehicle from running into an obstacle and to initiate an automatic braking process in the at least one following vehicle (60 to 120) in order to reduce the risk of collision between the leading vehicle and the at least one following vehicle (60 to 120), wherein a) in the leading vehicle a driver's warning is emitted when at least one warning condition is fulfilled, wherein b) the fulfilment of the warning condition indicates that owing to the instantaneous driving situation of the leading vehicle relative to the obstacle, the emergency braking operation must be initiated, wherein c) the automatic emergency braking process is only initiated in the leading vehicle after the driver's warning has been emitted and a warning time (tWarning) has then lapsed, wherein d) as the total warning time, the warning time comprises a first warning period (tWarning-Signal) and a second warning period (tPartialBrk), e) during the first warning period (tWamingSignal) visual and/or acoustic warning signals are emitted, and during the second warning period (tPartialBrk) that follows immediately after the first warning period (tWamingSignal) a partial braking of the leading vehicle with a partial braking deceleration is carried out, which is less severe than an emergency braking deceleration of the leading vehicle that takes place during the automatic emergency braking process, characterised in that f) in the at least one following vehicle (60 to 120) which is still in an un-braked condition, at the earliest at a first time point (ti) at which the first warning period (tWamingSignal) begins in the leading vehicle and at the latest at a second time point (t 2) at which the first warning period (tWamingSignal) ends in the leading vehicle, the automatic braking process is initiated, wherein g) in the at least one following vehicle, as the automatic braking a partial braking operation with a partial braking deceleration is initiated, which is less than a maximum possible emergency deceleration of the at least one following vehicle. a) in the leading vehicle a driver's warning is emitted when at least one warning condition is fulfilled, wherein b) the fulfilment of the warning condition indicates that owing to the instantaneous driving situation of the leading vehicle relative to the obstacle, the emergency braking operation must be initiated, wherein c) the automatic emergency braking process is only initiated in the leading vehicle after the driver's warning has been emitted and a warning time (tWarning) has then lapsed, wherein d) as the total warning time, the warning time comprises a first warning period (tWarning-Signal) and a second warning period (tPartialBrk), e) during the first warning period (tWamingSignal) visual and/or acoustic warning signals are emitted, and during the second warning period (tPartialBrk) that follows immediately after the first warning period (tWamingSignal) a partial braking of the leading vehicle with a partial braking deceleration is carried out, which is less severe than an emergency braking deceleration of the leading vehicle that takes place during the automatic emergency braking process, characterised in that f) in the at least one following vehicle (60 to 120) which is still in an un-braked condition, at the earliest at a first time point (ti) at which the first warning period (tWamingSignal) begins in the leading vehicle and at the latest at a second time point (t 2) at which the first warning period (tWamingSignal) ends in the leading vehicle, the automatic braking process is initiated, wherein g) in the at least one following vehicle, as the automatic braking a partial braking operation with a partial braking deceleration is initiated, which is less than a maximum possible emergency deceleration of the at least one following vehicle.