The main provisions of existing methods for estimating the delamination growth rates in layered composites under cyclic tension are presented. It is noted that the considered methods do not allow one to estimate the growth rates of various damage modes during the accumulation of fatigue. As a definite alternative to the presented methods, a methodology for such estimates is proposed using special rules of separate fatigue accumulation. Verification of the ratios of the proposed methodology is carried out on the example of calculated estimates of the growth rates of three damage modes (delamination, matrix cracking, and splitting and ply cracking around open hole edges) of three types of specimens made of laminates of various carbon plastics. It is noted that the accuracy of the obtained estimates depends on the accuracy of the approximation of the experimental data, on the basis of which the search for relations for the special rules of separate fatigue accumulation is conducted.