Particularly useful as a barrier layer in packaging, e.g. multilayer structures, is a composition based on an ethylene-vinyl alcohol copolymer comprising: 50 to 98% by weight of an EVOH copolymer 1 to 50% by weight of a polyethylene (A) 1 to 15% by weight of a polyethylene (B) being a blend of a polyethylene (B1) and a polyethylene (B2) chosen from elastomers, very-low-density polyethylenes and metallocene polyethylenes, the blend of (B1) and (B2) being cografted by an unsaturated carboxylic acid or a functional acid derivative thereof.