We analyse the effect of the applied field (Happl) on the current-driven magnetization reversal in pillar-shaped Co/Cu/Co trilayers, where we observe two different types of transition between the parallel (P) and antiparallel (AP) magnetic configurations of the Co layers. If Happl is weaker than a rather small threshold value, the transitions between P and AP are irreversible and relatively sharp. For Happl exceding the threshold value, the same transitions are progressive and reversible. We show that the criteria for the stability of the P and AP states and the experimentally observed behavior can be precisely accounted for by introducing the current-induced torque of the spin transfer models in a Landau-Lifschitz-Gilbert equation. This approach also provides a good description for the field dependence of the critical currents.