The stretched exponential (Williams-Watts) relaxation function is N* (t)=N* (0)exp<-(t/to)q>, 0<q≤1. As applied to aftershocks, N* (t) is the number of aftershocks that have not yet occurred at time t, starting with a finite number of potential events, N*(0). This function describes slow relaxation in a number of distinct physical systems. Whether it is the appropriate function for aftershocks, as an alternative to the modified Omori power law function, depends on the long-time behavior of the mean interevent time. The behavior of this function has been tested on synthetic sequences in comparison with the Omori relation to determine the feasibility of determining which is the better model of aftershock rate decay. The differences are practically indistinguishable for very slowly decaying sequences but are measurable for normally and rapidly decaying sequences if excellent data are available. Maximum likelihood estimates of the parameters in the stretched exponential function were determined for 29 sequences and the fit of the model to the data was compared with the modified Omori fit by the Akaike Information Criterion. If the time of the mainshock is taken as the start time for the sequence, the Omori fit is almost always better. If a later start time is used, 15 min to 2.5 hours for the cases tested, the stretched exponential fit is better in about half the cases. The selected start time is the time at which the rate of occurrence begins to decrease, after an initial apparent increase probably due to missed events during the very active interval. As expected, the relaxation time to is inversely related to the Omori p value and may prove to be more easily interpretable in terms of the physics of the aftershock-generating process. ¿ American Geophysical Union 1993