This paper consists of six sections of original contributions to the theory of cumulative fatigue damage of airframe structures and a section which consists of extensive bibliography of important papers in cumulative fatigue damage. Classical models for predicting the average number of cycles-to-failure, using basically one form or another of the so-called Miner’s rule, are known to be inadequate, in the sense that they either underestimate or overestimate, in some cases, the average number of cycles-to-failure. This is because they do not take into consideration, or even do not know how to take into consideration, the various co-occurring or concomitant factors, other than the various types of loads themselves, and incorporate them into the formula for predicting the expected number of cycles-to-failure. We believe that, in this paper we have suggested methods to circumvent the drawbacks from which the classical Miner’s rule suffers, and we have also offered models, in the more difficult and realistic situation, in which the additional increments in the propagation of the dominant crack form a dependent sequence of chance variables. It is the fond hope of the authors that they and other workers in the field will have the opportunity of applying the realistic approach to predicting the average number of cycles of a large airframe, based on actual flight test data, and to compare its performance with that of methods advanced in a follow-up effort.