The dynamics of a string of aircraft maintaining separation is investigated using a mathematical model in a serie of simulations. Three different separation criteria are considered -constant distance, constant time predictor and constant time delay -with four in-trail descent scenariostime-based or position-based top of descent, with or without speed reduction. The constant distance criteria exhibits best performance with a time-based top of descent, while for the constant time predictor and constant time delay criteria performs best with a position-based top of descent. The constant time delay criteria appears to be preferable on the overall since it requires the smallest speed variations to maintain the desired separation very accurately. Other configurations require larger speed variations that may be not desirable in real operations. In addition, by imposing an early descent in long string of aircraft, the time-based top of descent may be very inefficient. In the speed reduction scenarios, the constant time delay criteria induces oscillatory behaviour, which may result from the control law tuning. The sensitivity to the initial conditions and to the control law tuning is a major issue underlying the results of this study. This will be investigated in a more theoretical way and provided that robust gains can be identified, future work will then consist in investigating more varied vertical profiles.