A steerable structure (21, 27) of the catheter or endoscope type, the structure comprising an elastically or deformable longitudinal body (22, 28) including at least one actuator (16, 38) of material of the shape memory type incorporated longitudinally with the body (22, 28) together with Joule-effect heater means enabling the actuator (16, 38) to be contracted longitudinally in order to cause the longitudinal body (22, 28) to bend, wherein the actuator (16, 38) extends over at least one portion of the body (22, 28) that presents varying stiffness.