Load-controlled fatigue crack growth tests were carried out on two kinds of steels, S35C and SM50A, under constant amplitude loading and repeated two-step loading over a wide range from the linear elastic region to the post-yield one, and crack closure was investigated by using the minicomputer-aided unloading elastic compliance method.The fracture mechanics parameter, ΔJ/E(1-Jmax/C), was found to be a good parameter in expressing the fatigue crack growth rate under constant amplitude loadings irrespective of the stress ratios and materials, where ΔJ, Jmax, E and C are the J integral range, the maximum J integral, elastic modulus and a constant related to fracture toughness, respectively. However it was found that the constant, C, was not related to the elastic-plastic fracture toughness, JIc, but to the fracture toughness, Jc obtained using the same geometry specimens with identical crack length.The fatigue crack growth rate under repeated two-step loadings where both one-directional and cyclic plastic deformation were observed remarkably, could be well predicted by the linear summation rule of crack growth by using ΔJ*/E(1-Jmax/C), where ΔJ* is the J integral range-pair taking account of one-directional deformation under low-level loadings.