The crack propagation speed is an important parameter used to predict the life time of a part or a mechanical structure. Hence, in the last 50 years, many researchers have tried to explain and to create a mathematic model able to describe the phenomenon of fatigue crack initiation and propagation. In our days, the influence of the asymmetry coefficient having negative values, R, on the crack growth rate is considered an important issue. This paper presents theoretical aspects considered as basics for the NASGROS 5.0 software and the obtained results.