Studies were done to learn the role of some factors (nature of substrate, thickness of polymeric layer, presence of filler in the polymer) in the oxidation (the consumption rate of the antioxidant, the induction period) and adhesion strength (resistance to separation of coating from the substrate) of stabilized PE coatings. These factors lead to local zones in the coatings (in the polymer layer in contact with catalytically active substrates, near the filler particles, and in the outermost surface layer of the coatings oxidized under the conditions where oxygen was supplied by the diffusion mechanism) in which the antioxidant was consumed at an increased rate. The antioxidant consumed in these zones is replenished diffusively from the remaining part of the coating. A correspondence was observed between the induction period for oxidation of the polymer layer in contact with the substrate and the induction period for attaining adhesion (bonding) of the coating.