1. Many invasive species have rapidly adapted to different environments in their new ranges. This is surprising, as colonisation is usually associated with reduced genetic variation. Heritable phenotypic variation with an epigenetic basis may explain this paradox. 2. Here, we assessed the contribution of DNA methylation to local adaptation in native and naturalized non-native ruderal plant species in Germany. We reciprocally transplanted offspring from natural populations of seven native and five non-native plant species between the Konstanz region in the south and the Potsdam region in the north of Germany. Before the transplant, half of the seeds were treated with the demethylation agent zebularine. We recorded survival, flowering probability and biomass production as fitness estimates. 3. Contrary to our expectations, we found little evidence for local adaptation, both among the native and among the non-native plant species. Zebularine treatment had mostly negative effects on overall plant performance, regardless of whether plants were local or not, and regardless of whether they were native or non-native. 4. Synthesis. We conclude that local adaptation, at least at the scale of our study, plays no major role in the success of non-native and native ruderal plants. Consequently, we found no evidence yet for an epigenetic basis of local adaptation.