Abstract A theory of the fatigue process is given which enables the survival probability under general broad-band random loading to be calculated. In this theory the growth of fatigue damage is regarded as taking place continuously in time, rather than discretely, per cycle. The total damage increase in a time interval is obtained by integrating a damage-rate function over the interval for the particular stress—time curve which has operated. Forming averages over different stress-time functions for the random problem can then be carried out. For a normally-distributed random stress and a particular (realistic) damage-rate function we have calculated the mean damage, its standard deviation, and the survival function. We have also established that this approach gives good results for fixed-level tests.