We study the behavior of cytonuclear disequilibria in a finite monoecious population due to (1) random drift alone, (2) random drift and mutation, and (3) random drift and migration, using exact results on the RUZ (Random Union of Zygotes) model and diffusion approximations. We also show that the RUG (Random Union of Gametes) model is not suitable for a cytonuclear system. The study is also accompanied by a comparison with a two-locus nuclear system. We show that in a finite population of size N without mutation, the rate of decrease of the cytonuclear allelic disequilibrium is the same as that in the corresponding unlinked two-locus nuclear system. The principal rate of decrease of variance in allelic disequilibrium in a cytonuclear system is slightly faster than that in the corresponding nuclear system. However, the expected value of the variance in cytonuclear disequilibria is larger than that in a two-locus nuclear system for at least the first N generations. With mutation, the expected value of steady state variances of both systems are about the same; however, the normalized variance in linkage disequilibrium sigma 2d of the cytonuclear system is about twice as large as that for the corresponding nuclear system. For the migration process, two sets of steady state solutions are provided, one for the variables before migration and the other for the variables after migration. Diffusion approximations for both the principal rate of decay and steady state solutions in both systems are found to be satisfactory. A more accurate backward diffusion equation for a two-locus nuclear system is provided when the recombination fraction R is large.