Flexible endoscopic device, said device comprising an elongated flexible body with a flexible end segment that supports or forms the head of the endoscope, equipped with an optical system and able to be curved or bent in at least two mutually perpendicular directions, said elongated body being connected functionally at its other end to a control means for monitoring at least the movements and/or the arrangement of said end segment, said device also comprising automatic means for orienting and positioning the end segment by visual servoing, said means essentially consisting of a video processing device receiving video images or signals supplied by the optical system of the head of the endoscope by a computer means that can implement visual servo operations on the basis of processed video signals and providing control signals, and by actuating means (8, 8') that are part of or are associated with a control means for monitoring the end segment and receiving control signals supplied by the computer means, the means (6, 7, 8, 8', 12, 12') for automatically orientating and positioning the end segment being organised functionally to form at least one control loop that is designed to minimise error or an analogous measure of dissimilarity between on the one hand a target visual element or visual information extracted from a reference image and on the other hand a corresponding visual element or visual information extracted from the current image supplied by the optical system of the head of the endoscope, said error being used to deliver control signals to the actuating means (8, 8') monitoring the movements and the positioning of said end segment in at least one direction, the computer means being able, by executing a suitable program, to determine in real time, i.e. at least at the speed at which video images are supplied, an approximation, preferably by iterative processing, of the transformation to be applied to the current image so as to approach the latter from the reference image, the automatic positioning means (6, 7, 8, 8') being arranged in a bidimensional visual servo loop and comprising two independent actuators (8 and 8'), each controlling the movements and the positioning of the end segment according to any one of two mutually perpendicular directions corresponding to two directions of the current plane image provided by the head of the endoscope, the device being characterised in that the program executed by the computer means, within the context of servo operations, implements the approximation by minimising a cost function between a reduced image or thumbnail (T*) obtained from the reference image and a reduced image or thumbnail obtained from the current image supplied by the head of the endoscope and processed by the current approximated transformation, the reduced images or thumbnail images comprising target visual elements or visual information extracted from reference and current images and in that the control means comprises two concentric control axes (13 and 13') each connected to a control cable (12, 12') circulating along the elongated body and connected to the end segment to control the bending or the bowing of said segment according to one of two mutually perpendicular bending directions, the external axis being drive-related to a first actuator in the form of a motor with a hollow axis (8") by means of a disengaged transmission part in a central area extending into the continuity of the hollow axis (8") of said motor and the internal axis being in drive relation, by means of an elongated drive part with a second actuator in the form a motor aligned with the first motor according to their axes of rotation, said elongated drive part traversing the first motor at its hollow axis (8").