Abstract: A connection system between a slide and a very long member, allowing some longitudinal movement of said member in relation to the slide, corresponding to differential deformation, said slide being of the type which comprises a support provided with clamping parts which surround at least a part of said member. In accordance with the invention, the slide comprises, at the clamping zones, plates made of a material with a low coefficient of friction firstly on the surface of the support facing said member and secondly on the internal surface of each of said clamping parts. Application to connection systems for very long rails such as rails which carry travelling cranes and lateral guide rails for public transport vehicles.