A turbojet thrust reverser includes two doors each displaceable between an open position and a closed position of the reverser by at least one respective control actuator. Two electric motors drive the control actuators for the doors; each motor being controlled by an electronic control unit connected to a full authority digital engine control. Two servo-control devices control the displacement of the doors as a function of determined position references. The servo-control devices enable the doors to be displaced synchronously as a function of any variation in the forces exerted on the reverser and as a function of any force difference between the two doors.