Abstract: A Flight Management System for aircraft whereby time-constrained flight can be achieved while maintaining predetermined input parameters selected for minimizing cost of flight, wherein arbitrary points in the flight plan can be designated as time-constraint points, and wherein flight segments can be arbitrarily selected for exclusion from any speed variation. A speed generator derives an initial speed schedule for each segment of a flight plan from inputs of a predetermined cost index, the flight plan, and aircraft performance parameters. The speed schedule is modified by wind data, constant speed segments, and predetermined speed limits. When applied to a profile generator an estimated time of arrival is computed, as well as predicted distance and velocity values for each segment of flight. The predicted values are used to compute a total time of arrival.