Modern gas turbines utilize single crystal (SX) and directionally solidified (DS) nickel superalloys which hold a higher cyclic life resistance and an improved creep rupture strength compared to their conventionally cast (CC) version. Both, SX and DS materials feature a significant direction dependence of material properties, which needs to be considered in the constitutive and lifing models. In this context, the paper presents a mathematical framework of cyclic life prediction. Although the method is developed for DS nickel alloys with transverse isotropic material behaviour, a generalisation to common orthotropic materials inclu¬ding SX is straightforward. The proposed procedure is validated by two examples. Moreover, an application to turbine components is shown.