A coffee machine including a boiler for producing hot water and steam for the preparation of coffee or coffee-containing beverages. A coiled tubing is located in the boiler for producing hot milk or milk froth. Thus, no separate heating element is required for producing the hot milk or milk froth, as the milk or milk froth is heated by the water heated in the boiler for preparing the coffee. The coiled tubing is connected alternately to a milk container and a rinsing water source, so that potential milk residue is flushed out after each milk heating process. A predetermined amount of milk or rinsing water is fed to the coiled tubing by a pump. Thus the milk and rinsing water usage is optimized and the energy consumption is reduced.