BACKGROUND: Antagonistic species interactions can lead to coevolutionary genotype or phenotype frequency oscillations, with important implications for ecological and evolutionary processes. However, direct empirical evidence of such oscillations is rare. The rarity of observations is generally attributed to inherent difficulties of ecological and evolutionary long-term studies, to weak or absent interaction between species, or to the absence of negative frequency-dependence. RESULTS: Here, we show that another factor - non-genetic inheritance, mediated for example by epigenetic mechanisms - can completely eliminate oscillations in the presence of such negative frequency dependence, even if only a small fraction of offspring are affected. We analytically derive the threshold value of this fraction at which the dynamics change from oscillatory to stable, and investigate how selection, mutation and generation times differences between the two species affect the threshold value. These results strongly suggest that the lack of phenotype frequency oscillations should not be attributed to the lack of strong interactions between antagonistic species. CONCLUSIONS: Given increasing evidence of non-genetic effects on the outcomes of antagonistic species interactions, we suggest that these effects should be incorporated into ecological and evolutionary models of interacting species.