The EFSA Panel on Food Contact Materials, Enzymes and Processing Aids (CEP) assessed the safety of amines, di-C14-C18-alkyl, oxidised, renamed by the Panel as amines, di-C14-C20-alkyl, oxidised, from hydrogenated vegetable oil. The substance amines, bis(hydrogenated tallow alkyl) oxidised, consisting of the same components, but originating from tallow, is currently authorised as FCM substance No 768. The vegetable-sourced substance is intended to be used at up to 0.1% w/w as antioxidant and/or stabiliser in the manufacture of polyolefin food contact materials (FCM) and articles intended for contact with dry, aqueous and acidic foods. The substance is a mixture consisting of linear N,N-dialkyl hydroxylamines and their corresponding amine, nitrone and oxime derivatives, as well as further components: tert-N-oxides, secondary amides and carboxylic acids. Specific migration was tested from polyethylene samples in 10% ethanol and 3% acetic acid for 2 h at 100°C followed by 10 days at 60°C. None of the non-authorised components were detected to migrate at detection limits (LoD) in the range 0.003-0.029 mg/kg. The LoD of authorised carboxylic acids was 0.35 mg/kg. The Panel reassessed the genotoxicity studies carried out on FCM No 768 and evaluated two new bacterial reverse mutation tests on the nitrone and oxime derivatives as well as new (qualitative/quantitative) structure-activity relationship (Q)SAR analyses on other components. The Panel concluded that the substance did not raise a concern for genotoxicity. The Panel concluded that the substance is not of safety concern for the consumers if it is used as an additive at 0.1% w/w in the manufacture of polyolefin FCM intended to be in contact with foods simulated by food simulants A, B, C and E, except for infant formula and human milk, for storage above 6 months at room temperature and below, including hot-fill conditions and heating up to 100°C for 2 h.