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In this paper, push-pull fatigue tests of notched specimens under R = −1, 0 and 0.5 are carried out on annealed 0.1% carbon steel and quenched-tempered 0.5% carbon steel with H B 600. The fatigue limit of a long crack, σ w2 , is obtained from that of a notched specimen with a sharp and deep notch whose radius is smaller than the branch point ρ 0 . Using the present and past σ w2 data, the effect of the positive mean stress on the K w of the long crack is evaluated using 3.2H B ( σ B ) and σ S /(3.2H B ), where K w is the stress intensity factor range for predicting the fatigue limit of a metal with an arbitrary crack, σ S is the lower yield stress or 0.2 % proof stress, σ B is the ultimate tensile strength and H B is the Brinell hardness. Although the σ w2 decreases with the mean stress, σ w2 is cut off by the threshold stress σ we of the plastic deformation at the crack tip. For the quantitative prediction of the fatigue limit of a cracked steel with an arbitrary crack length under a positive mean stress, the σ w2 and σ we values are approximated by simple formulae.