The device may administer several infusions in sequence. The amount of each infusion, which is to be administered, is divided during the infusion time over a number of small portions. The supply of the various infusions is carried out alternately one after the other. The sequence of the infusions is so selected that infusions which react with one another or which are not compatible with one another are separated from one another by a buffer solution. This buffer solution can be in the form of a salt solution or a sugar solution. The buffer solution is also used to rinse the tubes of the infusion device.