Seed ageing is a complex process and can be described as the loss of viability or quality with time. It is important to elucidate whether genetic and epigenetic stability is altered in stored seeds and in seedlings produced from them. Non-stored and stored rye seeds at different stages of ageing were compared, as well as the seedlings obtained from them. Seeds were stored at 35 °C and 15% water content, under vacuum or air atmosphere. DNA of seeds and seedlings was isolated at three stages of the deterioration curve: P75 (13 days), P20 (29 days), and P0 (36 days). Genetic stability was assessed by RAPD technique, and epigenetic changes by MSAP markers. While seeds showed genetic stability after storage, the similarity of seedlings obtained from seeds stored for 29 days was lower (95%) when compared to seedlings from control seeds. Epigenetic changes were between 15% and 30% (both de novo methylation and demethylation) in the stored seeds compared to control seeds, with no differences between 13 and 29 days of storage with either air or vacuum atmospheres. In seedlings, epigenetic changes significantly increased with storage time. In conclusion, ageing increased epigenetic instability in both seeds and seedlings, when compared to controls.