Abstract: A process for managing air speed of an aircraft in flight. The method includes a first step of determining a point on the flight path at which it is theoretically possible to comply with a required time constraint by following a pre-established speed profile. In a second step, a speed is computed and a fresh speed profile is determined. This is obtained by determining speed corrections segment-by-segment from the point up to the last modifiable segment. The speed change in each segment is restricted to a maximum value. The new speed is computed on the basis of the curve showing the flight time t as a function of the speed V. This curve is approximated by a curve satisfying an equation with three coefficients (C.sub.1, C.sub.2, C.sub.3):V=c.sub.1 /t+c.sub.2 /t.sup.2 +c.sub.3 /t.sup.3Compliance with time constraints are ensured by this method while meeting the requirements of the pilot and air traffic controllers.