The present invention relates to an appliance for heating and/or frothingmilk, in whichsteam or a mixture of steam and air acting as a heat carrier is injected intothe milk, withthe heating unit comprising an inner steam channel (1) and an outer annularchannel (2)for the milk, where the outer annular channel coaxially surrounds the innersteamchannel, with hot steam or a mixture of steam and air being supplied at anupstream end(1a) of the steam channel (1) and with milk being supplied at an upstream end(2a) ofthe annular channel (2). To improve the heat output and the energy efficiencyof theheating unit and to reduce the maintenance requirement, the steam channel (1)and theannular channel (2) are separated from one another, with their downstream ends(1b, 2b)opening out into an outlet channel (3) for discharging the heated and/orfrothed milk.