An endoscope instrument includes an insertion tube of longitudinal axis possessing a proximal portion for connection to an actuation support and a distal portion presenting an outlet section occupied by a viewing zone and by at least one outlet orifice for passing at least one appliance for occupying a retracted position inside the tube and a working position in which the appliance occupies at least a portion of the outlet section. The distal portion of the insertion tube includes at least one radially deformable wall over a portion of its length extending from the outlet section, enabling the outlet section of the distal portion of the tube to be increased on the appliance passing from its retracted position in which the appliance does not stress the deformable wall to its working position in which the deformable wall is stressed radially.