In a device for dispensing milk and/or milk froth from a container (1) containing milk, this container is placed in a coolable cabinet (3). Via an extraction line (4) and a further line (5), the milk reaches an emulsifying device (6) disposed outside the coolable cabinet. The product received is dispensed from this emulsifying device (6) via the discharge nozzle (7). Steam is feedable into the emulsifying device (6) with which steam the milk conducted through the emulsifying device (6) is able to be heated up and/or frothed up. The further line (5) consists of a flexible tube which is placed in a peristaltic pump (9). This peristaltic pump (9) is equipped with switching means (10) with which the peristaltic pump (9) is switchable from a closed pump state into an open pump state releasing the passage of the flexible tube (5). Milk of different temperatures or milk froth can be optimally dispensed using this device; in addition an optimal cleaning can be carried out. This device is advantageously integrated into a coffee machine, making it possible to obtain automatically different types of coffee with added milk.