A device of electric connection between two successive sections of the ring-shaped pipe of a synchrotron, including: first and second end parts capable of being fastened to the sections, each including a tubular portion with facets; electrically-conductive resilient fingers, each of which bears on each of the two tubular portions while being able to slide on one of said facets; and at least one arm bearing on each finger, each arm being fixed with respect to one of the end parts.