This invention relates to a machine for dispensing beverages, e.g. tea or coffee, the operation of which is subject to the use of prepackaged one-cup pods. The machine (1) according to the invention comprises a revolving member (10), complete with a seat (13) for containing a pod, which cooperates with a hook (20), and a water heating and delivery unit (20) including a one-way flow valve (60) which is opened when a given pressure is exceeded. The water heating and delivery unit (30) is driven by an operating unit (50) to compress said pod when the revolving member (10) occupies the working position for the preparation and delivery of a beverage. The revolving member (10) subsequently completes a turn during which the pod contained in the seat (13) is removed by means of the hook (20).