Following a request from the European Commission, the Panel on Dietetic Products, Nutrition and Allergies was asked to provide a scientific opinion on a list of health claims pursuant to Article 13 of Regulation (EC) No 1924/2006. This opinion addresses the scientific substantiation of health claims in relation to walnuts and maintenance of normal blood LDL-cholesterol concentrations and improvement of endothelium-dependent vasodilation. The scientific substantiation is based on the information provided by the Member States in the consolidated list of Article 13 health claims and references that EFSA has received from Member States or directly from stakeholders. The food that is the subject of the health claims is walnuts. The Panel considers that walnuts are sufficiently characterised in relation to the claimed effects. Maintenance of normal blood LDL-cholesterol concentrations The claimed effects are "heart health (cardiovascular health)" and " lipid metabolism/heart health". The target population is assumed to be the general population. In the context of the proposed wordings and clarifications provided by Member States, it is assumed that the claimed effects refer to the maintenance of normal blood LDL-cholesterol concentrations. The Panel considers that maintenance of normal blood LDL-cholesterol concentrations is a beneficial physiological effect. In weighing the evidence, the Panel took into account that the evidence provided did not establish that consumption of walnuts had an effect on blood LDL-concentrations beyond what could be expected from their fatty acid composition, and that the LDL-cholesterol-lowering effect of walnuts could be attributed to their content of MUFAs and PUFAs. On the basis of the data presented, the Panel concludes that a cause and effect relationship has not been established between the consumption of walnuts and maintenance of normal blood LDL-cholesterol concentrations beyond what could be expected from the fatty acid composition of walnuts. A claim on the replacement of mixtures of SFAs with cis-MUFAs and/or cis-PUFAs in foods or diets and maintenance of normal blood LDL-cholesterol concentrations has already been assessed with a favourable outcome. A claim on linoleic acid and maintenance of blood cholesterol concentrations and a claim on alphalinolenic acid and maintenance of blood cholesterol concentrations have also already been assessed with favourable outcomes. Improvement of endothelium-dependent vasodilation The claimed effects are "well-balanced ratio of n-3- to n-6-fatty acids: artery and heart health lipid metabolism", and "artery health". The target population is assumed to be the general population. In the context of the proposed wordings and clarifications provided by Member States, it is assumed that the claimed effects refer to the improvement of endothelium-dependent vasodilation. The Panel considers that a sustained improvement of endothelium-dependent vasodilation may be a beneficial physiological effect. In weighing the evidence, the Panel took into account that one intervention study in healthy subjects, adequately powered and controlled, showed a sustained effect of the consumption of walnuts on endothelium-dependent vasodilation, that the results of one additional intervention study in type 2 diabetic subjects on blood pressure-lowering, cholesterol-lowering, and/or oral antidiabetic medication are consistent with these findings, and that an acute intervention study also showed a0 positive effect of the consumption of walnuts on endothelium-mediated vasodilation. The Panel concludes that a cause and effect relationship has been established between the consumption of walnuts and improvement of endothelium-dependent vasodilation. The Panel considers that in order to obtain the claimed effect, 30 g of walnuts should be consumed daily. These amounts can be consumed in the context of a balanced diet. The target population is the general population.