A vehicle door assembly may include a vehicle door pivotally arranged on a vehicle body, a drive motor for electromotively adjusting the vehicle door, a transmission element for producing a flux of force between the vehicle door and the vehicle body to adjust the vehicle door relative to the vehicle body, and a control device for controlling the drive motor. The control device may be configured to provide an anti-pinch protection. An acceleration sensor may be arranged on the vehicle door for measuring the acceleration of the vehicle door.