Uniparental inheritance of cytoplasmic elements is widespread among eukaryotic organisms and is achieved by a diverse range of mechanisms. This paper shows that the cytoplasmic genetic system would be expected to evolve towards uniparental inheritance, given the existence of deleterious symbionts capable of invading the host cytoplasm together with nuclear genes that lead to the elimination of cytoplasmic elements from one of the gamete types. The reason for this is that, under biparental inheritance, foreign symbionts with strong deleterious effects are able to spread through host populations. A nuclear modifier gene which leads to the loss of cytoplasmic elements from one gamete type gains a net advantage as a symbiont spreads, because the modifier sometimes gives rise to a symbiont-free zygote. Insofar as small gametes reduce the rate of symbiont transmission to the zygote, modifier genes causing small gamete size would tend to accumulate, so that cytoplasmic inheritance would become associated with maternal rather than paternal gametes. Once uniparental inheritance predominates in the host population, the population is protected from invasions by a large class of harmful symbionts, but at the same time those symbionts that benefit their hosts are still able to increase in frequency.