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Theoretical and empirical studies have shown that selection cannot maintain a joint nuclear-cytoplasmic polymorphism within a population except under restrictive conditions of frequency-dependent or sex-specific selection. These conclusions are based on fitness interactions between a diploid autosomal locus and a haploid cytoplasmic locus. We develop a model of joint transmission of X chromosomes and cytoplasms and through simulation show that nuclear-cytoplasmic polymorphisms can be maintained by selection on X-cytoplasm interactions. We test aspects of the model with a "diallel" experiment analyzing fitness interactions between pairwise combinations of X chromosomes and cytoplasms from wild strains of Drosophila melanogaster. Contrary to earlier autosomal studies, significant fitness interactions between X chromosomes and cytoplasms are detected among strains from within populations. The experiment further demonstrates significant sex-by-genotype interactions for mtDNA haplotype, cytoplasms, and X chromosomes. These interactions are sexually antagonistic--i.e., the "good" cytoplasms in females are "bad" in males--analogous to crossing reaction norms. The presence or absence of Wolbachia did not alter the significance of the fitness effects involving X chromosomes and cytoplasms but tended to reduce the significance of mtDNA fitness effects. The negative fitness correlations between the sexes demonstrated in our empirical study are consistent with the conditions that maintain cytoplasmic polymorphism in simulations. Our results suggest that fitness interactions with the sex chromosomes may account for some proportion of cytoplasmic variation in natural populations. Sexually antagonistic selection or reciprocally matched fitness effects of nuclear-cytoplasmic genotypes may be important components of cytonuclear fitness variation and have implications for mitochondrial disease phenotypes that differ between the sexes.