Method for producing a case-hardened steel component, namely a gear wheel, a shaft, an axle or a tool holder, in the case of which the steel component a) is shaped from a steel, which consists of in % by weight C: 0.1 - 0.30%, Si: 0 - 0.80%, Mn: 0.20 - 2.00%, Cr: 0 - 4.00%, Mo: 0.5 - 1.80%, N: 0.004 - 0.020%, S: 0 - 0.40%, Al: 0.004 - 0.020%, B: 0 - 0.0025% Nb: 0 - 0.20%, Ti: 0 - 0.02%, V: 0 - 0.40%, Ni: 0 - 0.5%, Cu: 0 - 0.3%, Co: 0 - 1.5% Remainder iron and unavoidable impurities which comprise in particular contents of P of up to 0.0035% by weight, wherein the Al content %AI, the Nb content %Nb, the Ti content %Ti, the V content %V and the N content %N of the steel meet the following condition: % Al / 27 + % Nb / 45 + % Ti / 48 + % V / 25 > % N / 3.5 and in which b) the steel component in question is case-hardened by b1) the steel component being held in a carburisation step for a duration of 150 min to 250 hours, at a temperature of 900 - 1050°C under a medium which contains carbon and optionally additionally nitrogen in order to produce a carburised or carbonitrided edge layer with a thickness of 0.3 - 15 μm on the steel component and after the carburisation step quickly being cooled to room temperature such that in the case of cooling the temperature range of 800 - 500°C is passed through within 6 - 600 seconds and b2) the steel component, in a hardening step completed after the carburisation step (work step b1), being heated to an austenitisation temperature which is at least 20°C above the Ac1 temperature and below the Ac3 temperature of the steel, of which the steel component consists, and proceeding from the austenitisation temperature being cooled at a cooling speed of 0.5 - 50 K/s to room temperature such that the obtained steel component has a thermochemically hardened edge layer and in its core region a structure, which is composed by at least 80% by volume of bainite, which consists of highly-tempered bainite originating from the structure, which the steel component comprised after case hardening (work step b.1) and before the hardening (work step b.2), and newly formed bainite and up to at most 20% by volume of residual austenite, ferrite, perlite or martensite. a) is shaped from a steel, which consists of in % by weight C: 0.1 - 0.30%, Si: 0 - 0.80%, Mn: 0.20 - 2.00%, Cr: 0 - 4.00%, Mo: 0.5 - 1.80%, N: 0.004 - 0.020%, S: 0 - 0.40%, Al: 0.004 - 0.020%, B: 0 - 0.0025% Nb: 0 - 0.20%, Ti: 0 - 0.02%, V: 0 - 0.40%, Ni: 0 - 0.5%, Cu: 0 - 0.3%, Co: 0 - 1.5% Remainder iron and unavoidable impurities which comprise in particular contents of P of up to 0.0035% by weight, wherein the Al content %AI, the Nb content %Nb, the Ti content %Ti, the V content %V and the N content %N of the steel meet the following condition: % Al / 27 + % Nb / 45 + % Ti / 48 + % V / 25 > % N / 3.5 and in which b) the steel component in question is case-hardened by b1) the steel component being held in a carburisation step for a duration of 150 min to 250 hours, at a temperature of 900 - 1050°C under a medium which contains carbon and optionally additionally nitrogen in order to produce a carburised or carbonitrided edge layer with a thickness of 0.3 - 15 μm on the steel component and after the carburisation step quickly being cooled to room temperature such that in the case of cooling the temperature range of 800 - 500°C is passed through within 6 - 600 seconds and b2) the steel component, in a hardening step completed after the carburisation step (work step b1), being heated to an austenitisation temperature which is at least 20°C above the Ac1 temperature and below the Ac3 temperature of the steel, of which the steel component consists, and proceeding from the austenitisation temperature being cooled at a cooling speed of 0.5 - 50 K/s to room temperature b1) the steel component being held in a carburisation step for a duration of 150 min to 250 hours, at a temperature of 900 - 1050°C under a medium which contains carbon and optionally additionally nitrogen in order to produce a carburised or carbonitrided edge layer with a thickness of 0.3 - 15 μm on the steel component and after the carburisation step quickly being cooled to room temperature such that in the case of cooling the temperature range of 800 - 500°C is passed through within 6 - 600 seconds and b2) the steel component, in a hardening step completed after the carburisation step (work step b1), being heated to an austenitisation temperature which is at least 20°C above the Ac1 temperature and below the Ac3 temperature of the steel, of which the steel component consists, and proceeding from the austenitisation temperature being cooled at a cooling speed of 0.5 - 50 K/s to room temperature