In a method for coordinating operation of motor vehicles driving fully automated, a trajectory described by a driving intervention is determined for each motor vehicle from status information of the motor vehicle, whereafter it is determined by an on-board vehicle system whether a coordination condition exists that requires coordination. If a coordination condition exists, trajectory data describing the trajectory are exchanged between the motor vehicles via a communication link through an on-board communication device and the trajectory is checked for conflicts caused by spatial and temporal overlap of the trajectories of at least two motor vehicles and/or because at least one of the motor vehicles did not reach its destination. If a conflict exists, the trajectory of a motor vehicle participating in the conflict is adjusted based on an arbitration rule evaluated by an arbitration device, whereafter the driving interventions described by the trajectory are performed by each motor vehicle.