A time constraint checking device performs a method for checking whether an aircraft is able to fulfill a plurality of successive time constraints corresponding to required times of arrival at a plurality of corresponding waypoints. The method includes comparing, for each of the waypoints, a comparison value depending on the time constraint with either an estimated time of arrival or minimum and maximum possible times of arrival based on speeds of the aircraft. The method performs different comparisons depending on whether the time constraints for a particular waypoint are a single time value or a time window, and an optimized time of arrival for meeting all future time constraints is also possible.