[4][5][6]. Also, there is a lack o f experimental data and theoretical generalization on crack propagation for a trapezoidal load cycle w ith various hold periods under m aximum load [7,8]. The m ajority of researchers in this case restrict them selves to the use o f the linear dam age sum m ation hypothesis based on the independent dam aging effect o f fatigue and creep [2,9]. Som etim es, they determ ine the m aterial susceptibility to a certain m ode o f fracture (fatigue or tim e-dependent) and, on this basis, choose the fracture m echanics param eters to describe experim ental crack grow th rate data [10,11]. It is notew orthy that such approaches do not always yield satisfactory results and require further experim ental and physical substantiation.E arlier [12,13], on the basis o f the experim ental data obtained and calculations perform ed, it was show n that the m ost com m only used approaches give no w ay o f predicting the crack grow th kinetics in the alloys under study to sufficient accuracy. In this paper, w e w ill discuss the m ethods proposed for the solution o f the above problem .R esea rch T ask S ta tem en t. H igh-tem perature nickel-based alloys EP742 and EP962 for aircraft applications w ere used as m odel m aterials. Their m echanical properties and other characteristics as w ell as the experim ental procedure w ere detailed earlier in [12,14]. The m aterials under study are used to m anufacture long-life aircraft gas-turbine engine (A G TE) disks. The service conditions (flight cycle) involve operation o f the m aterial under cyclic loading w ith long hold periods at m axim um load in a cycle. The solution o f this problem m akes it