Paramutation involves an interaction between homologous alleles resulting in a heritable change in gene expression without altering the DNA sequence. Initially believed to be restricted to plants, paramutation has recently been observed in animal models, and a paramutation-like event has been noted in humans. Despite the accumulating evidence suggesting that trans-acting epigenetic effects can be inherited transgenerationally and therefore generate non-genomic phenotypic variation, these effects have been largely ignored in the context of evolutionary theory. The model presented here incorporates paramutation into the standard model of viability selection at one locus and demonstrates that paramutation can create long-term biological diversity in the absence of genetic change, and even in the absence of the original paramutagenic allele. Therefore, if paramutation is present, attributing evolution to only a traditional genetic model may fail to encompass the broad scope of phenotypic differences observed in nature. Moreover, we show also that an unusual mathematical behaviour, analogous to "Ewens' gap" of the two-locus two-allele symmetric-selection model, occurs: when the rate of one parameter-for example, the rate of paramutation-is increased, a pair of equilibria may disappear only to reappear as this parameter increases further. In summary, by incorporating even the simplest epigenetic parameters into the standard population-genetic model of selection, we show how this type of inheritance system can profoundly alter the course of evolution.