The heat transfer surfaces of a condensation heat exchanger are provided with a coating according to the invention which comprises a sequence of layers which includes at least one hard layer which comprises amorphous carbon or a plasma polymer and at least one soft layer which comprises amorphous carbon or a plasma polymer. The hard and soft layers are applied alternately, the first layer on the heat transfer surface being a hard layer and the last layer of the coating being a soft layer. The last, soft layer is distinguished in particular by hydrophobic properties. The layer sequence ensures condensation of drops and, at the same time, protects against drop impingement erosion.