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 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 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 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 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.