The experimental data on the fatigue lives of crack growth that were obtained in tests of aluminum specimens with overloads and underloads in the region of near-threshold crack growth rates are compared. The fatigue crack growth time is predicted using various models, including those embedded in the NASGRO and FASTRAN software packages, in order to reveal the model that is the best for calculating the fatigue life. The results obtained are compared with the prediction of a proposed combined model, which takes into account crack closure and the local stresses in the crack mouth and is based on the Neuber and Ramberg–Osgood equations. The efficiencies of the existing and proposed models used to describe the growth of fatigue cracks during random loading are estimated.