After a brief account of theories currently put forward on damage accumulation, a modification of the best of these, the linear rule of damage accumulation, is presented. This theory is based on a new approach to the problem wherein the material behaviour in each of three different stress regions is analysed, in contrast to current approaches which endeavour to fit fatigue behaviour over the whole stress range into a single fundamental relation. In the three-region approach, evidence is given to show that the linear rule is effective in the intermediate stress levels of the S - log N relation, and that this region appears linear due to an exponential crack initiation theory, as opposed to present power function theories, which is based on prior history effects in plastic yielding. Non-linear damage activity is seen to modify this fundamental behaviour outside this stress region. To substantiate these theories, an experimental programme was undertaken using plain L.65 bar specimens. After establishing the S - N relation, a 'traverse' of the alternating stress range was made, cycling specimens at eight 'prestress' levels, each conforming in size to an envelope spectrum for a projected airliner, and then cycled at a datum level in the intermediate-stress region. From these results, the non-linear functions were estimated, and the final modified linear law developed. Specimen life under the spectrum was then calculated and compared with unmodified linear rule calculations. The results of the experimental tests, the background of the statistical methods used in assembling the data, and an assessment of the relative merits of three fillet designs are presented in Appendices.