System for fastening a rail in place on a base, - having a guide plate (1, 30) which has a supported surface by which it is supported on the base in the fitted position, a contacting surface which is associated with the foot of the rail which is to be fastened in place, and a through-opening which runs from its upper side to its supported surface, - having a clamping member which can be inserted through the through-opening in the guide plate (1, 30) and which can be fastened into the base, and - having a resilient member, which is in the fitted position braced against the base by means of the clamping member, and which is bent from a spring wire, characterised in that the resilient member - has at least one portion (22, 23) acting in torsion, which is exerting an elastic restorative force in the fitted position, - at one end of which is formed a first supporting portion (24, 25), which is aligned at an angle to the portion acting in torsion (22, 23) and which is in the fitted position supported on an associated support surface on the guide plate (1, 30) and - at the other end of which is formed a further supporting portion bent round from the portion (22, 23) acting in torsion, which is likewise supported on the guide plate (1, 30) in the fitted position and forms a fixed point for the torsion on the portion (22, 23) acting in torsion, wherein in the fitted position that end of the portion (22, 23) acting in torsion which is associated with the further supporting portion projects beyond the contacting surface of the guide plate (1, 30) towards the rail. - having a guide plate (1, 30) which has a supported surface by which it is supported on the base in the fitted position, a contacting surface which is associated with the foot of the rail which is to be fastened in place, and a through-opening which runs from its upper side to its supported surface, - having a clamping member which can be inserted through the through-opening in the guide plate (1, 30) and which can be fastened into the base, and - having a resilient member, which is in the fitted position braced against the base by means of the clamping member, and which is bent from a spring wire, characterised in that the resilient member - has at least one portion (22, 23) acting in torsion, which is exerting an elastic restorative force in the fitted position, - at one end of which is formed a first supporting portion (24, 25), which is aligned at an angle to the portion acting in torsion (22, 23) and which is in the fitted position supported on an associated support surface on the guide plate (1, 30) and - at the other end of which is formed a further supporting portion bent round from the portion (22, 23) acting in torsion, which is likewise supported on the guide plate (1, 30) in the fitted position and forms a fixed point for the torsion on the portion (22, 23) acting in torsion, wherein in the fitted position that end of the portion (22, 23) acting in torsion which is associated with the further supporting portion projects beyond the contacting surface of the guide plate (1, 30) towards the rail. - has at least one portion (22, 23) acting in torsion, which is exerting an elastic restorative force in the fitted position, - at one end of which is formed a first supporting portion (24, 25), which is aligned at an angle to the portion acting in torsion (22, 23) and which is in the fitted position supported on an associated support surface on the guide plate (1, 30) and - at the other end of which is formed a further supporting portion bent round from the portion (22, 23) acting in torsion, which is likewise supported on the guide plate (1, 30) in the fitted position and forms a fixed point for the torsion on the portion (22, 23) acting in torsion, wherein in the fitted position that end of the portion (22, 23) acting in torsion which is associated with the further supporting portion projects beyond the contacting surface of the guide plate (1, 30) towards the rail. - at one end of which is formed a first supporting portion (24, 25), which is aligned at an angle to the portion acting in torsion (22, 23) and which is in the fitted position supported on an associated support surface on the guide plate (1, 30) and - at the other end of which is formed a further supporting portion bent round from the portion (22, 23) acting in torsion, which is likewise supported on the guide plate (1, 30) in the fitted position and forms a fixed point for the torsion on the portion (22, 23) acting in torsion, wherein in the fitted position that end of the portion (22, 23) acting in torsion which is associated with the further supporting portion projects beyond the contacting surface of the guide plate (1, 30) towards the rail.