A method for assembling parts in an assembly line, such as an automotive final assembly line, comprising: - advancing a part along the assembly line with an Automated Guided Vehicle AGV, the part having a target area at which an assembly operation is to be performed; - arranging a first real time vision system to monitor the position of the AGV in at least two directions, the first real time vision system being provided with a vision sensor mounted stationary in the assembly line, the vision sensor of the first real time vision system being configured to track the movement of the AGV in an assembly line advance direction and in a vertical direction; - providing the readings of the first real time vision system to a robot controller arranged to control an assembly unit of the assembly line to perform an automated operation on the part that is advanced or supported by the AGV, the assembly unit comprising an industrial robot that is provided with an end effector; - arranging a second real time vision system to monitor the position of the target area, the second real time vision system comprising a vision sensor mounted on the robot so that it moves together with the end effector; wherein, while the part is advancing, - the readings of the first real time vision system are provided to the robot controller to synchronise the displacement of the robot or of the end effector of the robot with the advance of the AGV along the assembly line in the advance direction, and to synchronize the displacement of the end effector of the robot in the vertical direction with vertical oscillations of the AGV; and - the assembly operation at the target area is performed with the industrial robot and comprises: - a visual servoing process in which the movement of the end effector of the robot is controlled in real time based at least on the readings of the second real time vision system, and - a compliant behaviour process in which the movement of the end effector of the robot is controlled at least to allow compliant behaviour of the end effector in at least one direction. - advancing a part along the assembly line with an Automated Guided Vehicle AGV, the part having a target area at which an assembly operation is to be performed; - arranging a first real time vision system to monitor the position of the AGV in at least two directions, the first real time vision system being provided with a vision sensor mounted stationary in the assembly line, the vision sensor of the first real time vision system being configured to track the movement of the AGV in an assembly line advance direction and in a vertical direction; - providing the readings of the first real time vision system to a robot controller arranged to control an assembly unit of the assembly line to perform an automated operation on the part that is advanced or supported by the AGV, the assembly unit comprising an industrial robot that is provided with an end effector; - arranging a second real time vision system to monitor the position of the target area, the second real time vision system comprising a vision sensor mounted on the robot so that it moves together with the end effector; wherein, while the part is advancing, - the readings of the first real time vision system are provided to the robot controller to synchronise the displacement of the robot or of the end effector of the robot with the advance of the AGV along the assembly line in the advance direction, and to synchronize the displacement of the end effector of the robot in the vertical direction with vertical oscillations of the AGV; and - the assembly operation at the target area is performed with the industrial robot and comprises: - a visual servoing process in which the movement of the end effector of the robot is controlled in real time based at least on the readings of the second real time vision system, and - a compliant behaviour process in which the movement of the end effector of the robot is controlled at least to allow compliant behaviour of the end effector in at least one direction. - a visual servoing process in which the movement of the end effector of the robot is controlled in real time based at least on the readings of the second real time vision system, and - a compliant behaviour process in which the movement of the end effector of the robot is controlled at least to allow compliant behaviour of the end effector in at least one direction.