  A geodynamo-model based on an \alpha-effect which has been computed under
conditions suitable for the geodynamo is constructed. For a highly restricted
class of radial \alpha-profiles the linear \alpha2-model exhibits oscillating
solutions on a timescale given by the turbulent diffusion time. The basic
properties of the periodic solutions are presented and the influence of the
inner core size on the characteristics of the critical range that allows for
oscillating solutions is shown. Reversals are interpreted as half of such an
oscillation. They are rather seldom events because they can only occur if the
\alpha-profile exists long enough within the small critical range that allows
for periodic solutions. Due to strong fluctuations on the convective timescale
the probability of such a reversal is very small. Finally, a simple non-linear
mean-field model with reasonable input parameters based on simulations of
Giesecke et al. (2005) demonstrates the plausibility of the presented theory
with a long-time series of a (geo-)dynamo reversal sequence.
