The concepts and results of several theories of localized spin fluctuations are contrasted. The random phase approximation-qualitatively correct for weak exchange coupling U-overemphasizes the collective nature of the fluctuations and in dilute alloys leads to an unphysical instability for U ≥ Uc. For U ~ Uc, nonlinear interactions between spin fluctuations suppress the instability. The se anharmonic effects have been treated through the functional average and the diagram summation schemes, and they lead to a smooth variation of the system properties as U increases through Uc. A complementary treatment in which we study the time-evolution of spin fluctuations is also considered