Abstract: A set of connecting accessories for an electrical supply rail with an asymmetrical profile, comprising a first main accessory called a "line connector" enables the conductors of two rails to be connected electrically, no matter whether the link be on the right or the left of the rail, without it being necessary to have a fool proofing device, a second accessory called "universal supply box," and a third accessory called "connecting block". The combination of such a set of accessories making it possible with a minimum number of elements of different kinds to produce, with an asymmetrical type rail, all the assembly figures : straight line, T shape, L shape, cross shape.