<b>ABSTRACT</b></br>

A fatigue process due to random loading that is progressively damaging a certain structural detail will vary in the presence of mean stresses. The variations are already considered in crack propagation laws and by applying equivalent 0-mean stress ranges from the Palmgren–Miner linear rule. Nevertheless, if the mean stress is intrinsic, instead of a direct consequence of the random loading, other second-order effects will have to be taken into account. Those effects are cycle quasi-ordering, histogram variations, and apparent mean tension, which are identified and defined in this study and, finally, developed in a case study for demonstrative purposes.</br>

<b>ACKNOWLEDGEMENTS</b></br>

The authors would like to thank and extend their warm recognition to Mr. Asier Maiztegi Eriz, for establishing and managing the framework within Tecnalia that made the PhD Thesis possible that is summarized in this paper. (Thank you Asier, you were not the only one with eyes, but certainly the only one with a view).