A method of controlling the arrival of an aircraft at a target waypoint, comprising (a) defining a required time of arrival (RTA) at that target waypoint; (b) obtaining a prediction of the aircraft trajectory and an estimate of time of arrival (ETA) of the aircraft at the target waypoint, the estimate being carried out at an intermediate waypoint prior to the target waypoint, wherein a first plurality of intermediate waypoints lies within a first phase of the aircraft flight trajectory to the target waypoint, and wherein a second plurality of intermediate waypoints lies within a second phase of the aircraft flight trajectory to the target waypoint, wherein the first phase of the aircraft flight trajectory is a cruise phase whilst the second phase of the aircraft flight trajectory is a descent phase that follows a Top of Descent (TOD) position; (c) calculating a difference between RTA and ETA for each intermediate waypoint; (d) determining if |RTA - ETA| exceeds a difference threshold (DT) for each intermediate waypoint; (e) where the intermediate waypoint lies within the said first phase of the aircraft flight trajectory, and where |RTA - ETA| > DT, adjusting the commanded flight speeds during that first phase of the aircraft flight trajectory whilst maintaining, unadjusted, flight speeds of the predicted aircraft trajectory during the second phase of the aircraft flight trajectory; (f) where the intermediate waypoint lies within the said second phase of the aircraft flight trajectory, and where |RTA - ETA| > DT, adjusting the commanded flight speeds during that second phase of the aircraft flight trajectory; and (g) executing a new trajectory and associated flight plan based upon the adjusted commanded flight speeds, so as to command the aircraft to follow the new speed schedule. (a) defining a required time of arrival (RTA) at that target waypoint; (b) obtaining a prediction of the aircraft trajectory and an estimate of time of arrival (ETA) of the aircraft at the target waypoint, the estimate being carried out at an intermediate waypoint prior to the target waypoint, wherein a first plurality of intermediate waypoints lies within a first phase of the aircraft flight trajectory to the target waypoint, and wherein a second plurality of intermediate waypoints lies within a second phase of the aircraft flight trajectory to the target waypoint, wherein the first phase of the aircraft flight trajectory is a cruise phase whilst the second phase of the aircraft flight trajectory is a descent phase that follows a Top of Descent (TOD) position; (c) calculating a difference between RTA and ETA for each intermediate waypoint; (d) determining if |RTA - ETA| exceeds a difference threshold (DT) for each intermediate waypoint; (e) where the intermediate waypoint lies within the said first phase of the aircraft flight trajectory, and where |RTA - ETA| > DT, adjusting the commanded flight speeds during that first phase of the aircraft flight trajectory whilst maintaining, unadjusted, flight speeds of the predicted aircraft trajectory during the second phase of the aircraft flight trajectory; (f) where the intermediate waypoint lies within the said second phase of the aircraft flight trajectory, and where |RTA - ETA| > DT, adjusting the commanded flight speeds during that second phase of the aircraft flight trajectory; and (g) executing a new trajectory and associated flight plan based upon the adjusted commanded flight speeds, so as to command the aircraft to follow the new speed schedule. <EOS>