Parking assistance system which can be remotely controlled from outside a motor vehicle and has a remotely controllable parking function for automated parking in and exiting from a parking space (20, 21), which system permits parking in the forward parking direction or in the reverse parking direction depending on the position of the parking space (20, 21), wherein the parking assistance system comprises: - a receiving device for receiving a movement direction of the vehicle, as selected by the user, wherein it is possible to receive as a selected movement direction: • a forward-driving movement direction for driving the vehicle forward and • a reverse-driving movement direction for driving the vehicle in reverse, and - a control device which is coupled to the receiving device and is configured • to decide independently whether a parking situation or a parking-space-exiting situation is present, • when the presence of a parking situation is detected, to park the vehicle in accordance with the received selected movement direction by driving forward or driving in reverse into the parking space (20, 21), and • when the presence of a parking-space-exiting situation is detected, to make the vehicle exit the parking space (20, 21) in accordance with the received selected movement direction by driving forward or driving in reverse, wherein the control device is also configured - to detect a change in position of the vehicle with respect to a parking position of the vehicle in which the vehicle has been parked without using the remotely controllable parking function, and - to decide independently, on the basis of the detected change in position and the received selected movement direction, whether a parking situation or a parking-space-exiting situation is present. - a receiving device for receiving a movement direction of the vehicle, as selected by the user, wherein it is possible to receive as a selected movement direction: • a forward-driving movement direction for driving the vehicle forward and • a reverse-driving movement direction for driving the vehicle in reverse, and - a control device which is coupled to the receiving device and is configured • to decide independently whether a parking situation or a parking-space-exiting situation is present, • when the presence of a parking situation is detected, to park the vehicle in accordance with the received selected movement direction by driving forward or driving in reverse into the parking space (20, 21), and • when the presence of a parking-space-exiting situation is detected, to make the vehicle exit the parking space (20, 21) in accordance with the received selected movement direction by driving forward or driving in reverse, • a forward-driving movement direction for driving the vehicle forward and • a reverse-driving movement direction for driving the vehicle in reverse, and - a control device which is coupled to the receiving device and is configured - a control device which is coupled to the receiving device and is configured • to decide independently whether a parking situation or a parking-space-exiting situation is present, • when the presence of a parking situation is detected, to park the vehicle in accordance with the received selected movement direction by driving forward or driving in reverse into the parking space (20, 21), and • when the presence of a parking-space-exiting situation is detected, to make the vehicle exit the parking space (20, 21) in accordance with the received selected movement direction by driving forward or driving in reverse, - to detect a change in position of the vehicle with respect to a parking position of the vehicle in which the vehicle has been parked without using the remotely controllable parking function, and - to decide independently, on the basis of the detected change in position and the received selected movement direction, whether a parking situation or a parking-space-exiting situation is present.