Abstract: Improvement of equipment for attaching trailers with inertia controlled braking arrangement, being of the type including stabilizing bars whose exposure to tension provides an coupling arrangement for nullifying the reaction force affecting the supports of the movable control components. This reaction force results from inertia brake in the trailer and creates an increasing adverse force affecting said movable components. Characteristic is that this adverse force is generated by two elastically deformable arms freely articulated on a common axle located at the end of the coupling seat of the trailer. The free ends of either of these arms, usually curved downwards, is in permanent elastic abutment with the corresponding attachment bar. Elements are provided for keeping the arms on the bars during traction, turning and braking.