For the application of a scratch protection layer on plastic substrates, a plasma is produced by the plasma CVD method, away from the individual plastic substrate, in an excitation gas, and this excitation gas is supplied through a tube to the plastic substrate. Subsequently, an antireflection layer is applied by means of a gas flow sputter source. The apparatus provided for this has a plasma CVD chamber (1) and a gas flow sputter chamber (2), next to one another. The plastic substrates (7,8) to be coated are transported from the plasma CVD chamber (2) to the gas flow sputter chamber (1) with the aid of a transporting device (3), designed as a turning plate.