Fastening system for a machine element (41), in particular for an elongate machine element (41), in particular for a toothed rack or a linear guide, for fastening in an abutment (45), in particular a machine bed or a flange, comprising: an eccentric bolt (1) which comprises a pin section (5) to be received in a receiving opening (55) of an abutment (45) and comprises a joining section (7), wherein the joining section is arranged in an eccentric manner in relation to the pin section (5), and an eccentric sleeve (3) to be slid onto the joining section (7).