The single-and multiple-electron loss of fast highly charged projectiles in collisions with neutral molecules is studied within the framework of a nonperturbative approach. The cross sections for single-, double-, and triple-electron losses are calculated for the collision system Fe q+ → N 2 (q = 24, 25, 26) at the collision energies 10, 100, and 1000 MeV/nucleon. The effects caused by the collision multiplicity and the orientation of the axis of the target molecule are treated. It is shown that the collision multiplicity effect leads to considerable differences for the cases of perpendicular and parallel orientations of the molecular axes with respect to the direction of the projectile motion, while for chaotic orientation such an effect is negligible.