Author summary Evolution is known to occur because of changes in DNA sequence which are inherited between generations. Recently, though, it has been discovered that information beyond the DNA sequence can be transmitted between generations. This information, known as epigenetic, can control how the DNA sequence is used. Epigenetic information that is transmitted between generations could drive evolutionary processes in populations, but this is yet to be tested. We used a simple nematode worm to investigate the contribution of different types of epigenetic information to evolution. We evolved populations of worms in the laboratory and investigated epigenetic differences that emerged in different lineages. Most epigenetic differences were very short-lived, so unlikely to be able to contribute to long-term evolutionary processes. However, we identified some changes that lasted much longer. Intriguingly, genes that control the worms’ responses to external threats such as bacterial infections or noxious chemicals were most likely to undergo long-term epigenetic changes, despite the fact that the environment of the worms was stable and did not contain these stresses. We think that epigenetic processes might be able to create a fast-acting form of variation that could help in situations where organisms need to adapt to dangerous environments.