The tea or coffee maker has a heat source (16) for heating the water in a fresh water container (1), the heated water supplied via a riser pipe (7) to a filter (11) containing ground coffee or tea leaves, supported above a reception jug (19). A valve (4) blocks the reverse flow of water to the fresh water container.The heat source is heated by a boiler (2) with a vol. which is a fraction of the vol of the fresh water container and is coupled to the base of the container via a coupling line (3) including the non-return valve (4), blocked when the boiler is filled and by the steam pressure in the boiler.