The basic principles underlying the single-domain theory developed by N¿el are examined using a modern statistical mechanics approach. It is shown that the quasi-equilibrium theory of N¿el is in good shape but there are problems with the dynamic part of the theory. The physical assumptions made with regard to ''thermal fluctuations'' appear oversimplified, and N¿el's theory, and a similar theory by Brown, violate the detailed balance theorem of statistical mechanics. These problems deal only with the attempt frequency factor used in estimations of the relaxation time and not with the important exponential factor, which appears to have been correctly determined by N¿el. In the absence of a convincing theory for the attempt frequency factor, it is recommended that experimental values be used (107 to 108 s-1 for magnetite). Although N¿el's theory does appear to be correct in identifying the critical exponent dependence of the relaxation times as a function of activation energy and temperature, the activation energy values used by paleomagnetists in applying N¿el's theory are often incorrect, as has been previously pointed out by Smith. Consistent with Smith's suggestion, lower activation energies are obtained by modeling noncoherent reversal modes with the passage of a domain wall. This leads to a significant lowering of the activation energy in most cases. However, the resulting activation energy still appears to be somewhat too high based on experimental evidence, indicating that either defects play an important role and/or other modes of noncoherent rotation occur (including other possible domain wall structures) in practice. ¿ American Geophysical Union 1988