In Saccharomyces cerevisiae, previous studies on the inheritance of mitochondrial genes controlling antibiotic resistance have shown that some crosses produce a substantial number of uniparental zygotes, which transmit to their diploid progeny mitochondrial alleles from only one parent. In this paper, we show that uniparental zygotes are formed especially when one parent (majority parent) contributes substantially more mitochondrial DNA molecules to the zygote than does the other (minority) parent. Cellular contents of mitochondrial DNA (mtDNA) are increased in these experiments by treatment with cycloheximide, alpha-factor, or the uvsp5 nuclear mutation. In such a biased cross, some zygotes are uniparental for mitochondrial alleles from the majority parent, and the frequency of such zygotes increases with increasing bias. In two- and three-factor crosses the cap1, ery1, and oli1 loci behave coordinately, rather than independently; minority markers tend to be transmitted or lost as a unit, suggesting that the uniparental mechanism acts on entire mtDNA molecules rather than on individual loci. This rules out the possibility that uniparental inheritance can be explained by the conversion of minority markers to the majority alleles during recombination. Exceptions to the coordinate behavior of different loci can be explained by marker rescue via recombination. Uniparental inheritance is largely independent of the position of buds on the zygote. We conclude that it is due to the failure of minority markers to replicate in some zygotes, possibly involving the rapid enzymatic destruction of such markers. We have considered two general classes of mechanisms: (1) random selection of molecules for replication, as for example by competition for replicating sites on a membrane; and (2) differential marking of mtDNA molecules in the two parents, possibly by modification enzymes, followed by a mechanism that "counts" molecules and replicates only the majority type. These classes of models are distinguished genetically by the fact that the first predicts that the output frequency of a given allele among the progeny of a large number of zygotes will approximately equal the average input frequency of that allele, while the second class predicts that any input bias will be amplified in the output. The data suggest that bias amplification does occur. We hypothesize that maternal inheritance of mitochondrial or chloroplast genes in many organisms may depend upon a biased input of organelle DNA molecules, which usually favors the maternal parent, followed by failure of the minority (paternal) molecules to replicate in many or all zygotes.