The present invention relates to a system and to a fastening of a rail 2 on a substrate U, with a guide plate 13, 14 which is provided for laterally guiding the rail 2 and has a standing surface associated with the substrate U, with a support element 20, 21 which is provided to support the guide plate 13, 14 in the assembly position, on its side remote from the rail 2, against a stop 4, 5 and has for this purpose an abutment surface 22 associated with the guide plate 13, 14 and a support surface 23 associated with the stop 4, 5, with a spring element 17a, 17b which is provided to be supported on the guide plate 13, 14 and at least one spring arm for exerting a resilient holding force onto the foot of the rail 2, and with a tensioning means 18, 19 for tensioning the spring element 17a, 17b. The fastening can be assembled in a particularly simple manner in that the support element 20, 21 has a support lug 32a - 32d which is provided to be supported on the substrate U in the assembly position and in the process to reach under the standing surface of the guide plate 13, 14 in such a way that the guide plate 13, 14 is supported on the substrate U via the support lug 32a - 32d in the region in which the guide plate 13, 14 and support lug 32a - 32d overlap.