Method for closed loop longitudinal control of a vehicle according to a target trajectory (T soll ) which specifies a series of target positions (P k ) to be assumed by the vehicle over time (t), wherein - an actual state (Z) of the vehicle is taken as a basis for determining a control acceleration (a ctrl_trj ) for closed loop trajectory control by means of which the vehicle is supposed to be accelerated in accordance with specifications of the target trajectory (T soll ), - an actual velocity (v ist ) of the vehicle and a specified maximum velocity (v max ) which is not supposed to be exceeded when travelling along the target trajectory (T soll ) are taken as a basis for determining a control acceleration (a ctrl_v ) for closed loop velocity control by means of which the vehicle is supposed to be accelerated in order to guide it at the maximum velocity (v max ), - the two control accelerations (a ctrl_trj , a ctrl_v ) are supplied to an arbiter (5.3) which uses them to determine a resulting control acceleration (a ctrl ), - the vehicle is accelerated in accordance with the resulting control acceleration (a ctrl ), - the specified maximum velocity (v max ) is determined from a minimum from a maximum trajectory velocity (v max_orth ), a legally permissible maximum velocity (v max_legal ) and an absolute system-defined maximum velocity (v max_sys ), - the maximum trajectory velocity (v max_orth )is determined from a sum of a local reference velocity (v refPtOrth ), specified in the target trajectory (T soll ), at an actual position (P ist ) of the vehicle and a maximum permitted deviation (Δv) of the local reference velocity (v refPtOrth ) according to the actual velocity (v ist ) and a curvature (K) of the target trajectory (T soll ) at the actual position (P ist ) of the vehicle and - the absolute system-defined maximum velocity (v max_sys ) is specified as a system restriction in the form of a maximum velocity defined for the vehicle in a system intended for automated control of the vehicle. - an actual state (Z) of the vehicle is taken as a basis for determining a control acceleration (a ctrl_trj ) for closed loop trajectory control by means of which the vehicle is supposed to be accelerated in accordance with specifications of the target trajectory (T soll ), - an actual velocity (v ist ) of the vehicle and a specified maximum velocity (v max ) which is not supposed to be exceeded when travelling along the target trajectory (T soll ) are taken as a basis for determining a control acceleration (a ctrl_v ) for closed loop velocity control by means of which the vehicle is supposed to be accelerated in order to guide it at the maximum velocity (v max ), - the two control accelerations (a ctrl_trj , a ctrl_v ) are supplied to an arbiter (5.3) which uses them to determine a resulting control acceleration (a ctrl ), - the vehicle is accelerated in accordance with the resulting control acceleration (a ctrl ), - the specified maximum velocity (v max ) is determined from a minimum from a maximum trajectory velocity (v max_orth ), a legally permissible maximum velocity (v max_legal ) and an absolute system-defined maximum velocity (v max_sys ), - the maximum trajectory velocity (v max_orth )is determined from a sum of a local reference velocity (v refPtOrth ), specified in the target trajectory (T soll ), at an actual position (P ist ) of the vehicle and a maximum permitted deviation (Δv) of the local reference velocity (v refPtOrth ) according to the actual velocity (v ist ) and a curvature (K) of the target trajectory (T soll ) at the actual position (P ist ) of the vehicle and - the absolute system-defined maximum velocity (v max_sys ) is specified as a system restriction in the form of a maximum velocity defined for the vehicle in a system intended for automated control of the vehicle. <EOS>