The invention concerns the fixing of a bearing shaft (6) in a reception bore (1.3) of a housing, at least one end of the shaft being adapted to be swaged to the reception bore (1.3) for achieving at least one of a force locking and a positive engagement, and an outer peripheral surface of the shaft (6) having a hardness that is greater than a hardness of the ends (6.2) of the shaft. The novel shaft is carbonitrided, quenched and tempered so that at first a hardness of HV 745-950 (HRC 62-68) is realized, following which the thus treated shaft (6) is soft annealed to produce a hardness of HV 212-305 (HRB 93-HRC30), and the outer peripheral surface is then subjected to induction hardening to achieve a final hardness of HV 745-950 (HRC 62-68). The shaft of the invention has a long operating life even under high load conditions.