Summary Twenty‐four dairy sheep and goats, respectively, were assigned each to three homogenous subgroups per animal species and fed the same diet in quantities which met 70% (underfeeding), 100% (control) and 130% (overfeeding) of their energy and crude protein requirements. The results showed that the underfed sheep in comparison with the control had significantly lower glutathione reductase (GR), superoxide dismutase (SOD), catalase and glutathione peroxidase (GPX) activities and total antioxidant capacity (measured with Ferric Reducing Ability of Plasma FRAP assay) in their blood plasma. A significant increase in the glutathione transferase (GST) and GPX activities, malondialdehyde content and total antioxidant capacity (measured with 2,2′‐azino‐bis(3‐ethylbenzothiazoline‐6‐sulphonic acid) ABTS assay) in the blood plasma of underfed goats compared with controls was observed, while the opposite happened for the GR and SOD activities. The underfeeding in both animal species caused a significant increase in the protein carbonyls (PC) content of their blood plasma. The overfeeding, compared with the control, caused a significant decline in the GPX activity and total antioxidant capacity (measured with FRAP) in the blood plasma of sheep while the opposite happened for the GPX and GST activities in the case of goats. The overfed animals, of both species, compared with the respective controls, had higher PC content in their blood plasma. The feeding level had no noticeable impact on the antioxidants' enzymes activities of milk in both animal species. Moreover, the underfeeding in the blood plasma and the overfeeding in milk of both animal species resulted into a significant increase in the PC content. Finally, only in sheep milk, the underfeeding, compared with the respective control, and overfeeding reduced significantly the total antioxidant capacity (measured with ABTS). The feeding level caused oxidative stress in both organism and milk but the response was different in animal species and needs further investigation.