The invention provides a system for fastening a rail in place and a rail fastener which, while being simple to install, allow a large measure of freedom in the production of the components required and at the same time have great practical utility. To this end a system according to the invention for fastening a rail to a fixed bottom support comprises: a base plate produced from a plastics material, an intermediate layer which is arranged between the base plate and the fixed bottom support, a carrier plate which is arranged between the intermediate layer and the bottom support, a resilient member to hold down the rail which is to be fastened in place, a clamping bolt to brace the resilient member against the base plate, and a fastening member for fastening the base plate to the fixed bottom support.