Time-varying statistics of geomagnetic reversal sequences are examined to test the hypothesis that reversals are generated by a gamma renewal process. Although gross statisticl properties of the observations support this model, the statistics of normal polarity intervals are found to differ significantly from those of reversed polarity intervals. This asymmetry, which is not predicted by theoretical dynamo or reversal mechanisms, can be related to the relative stability of normal and reversed states. The reversed state is found to be less stable in the period immediately following a reversal. On the basis of these resuts the simplest stochastic model describing reversals would be an alternating renewal process with a time-varying mean and gamma-distributed polarity intervals.