The invention concerns a cartridge-operated coffee-machine, comprising means for supplying hot water to an infusion head adapted to receive at least two different cartridges (2, 2′) including each at least one planar seat surface, means for communicating said supply means with the product contained inside the cartridges so as to obtain a beverage, and means for directing said beverage exiting from the cartridge towards a beverage collecting receptacle, where the infusion head comprises a support (11) having at least one pocket (29) forming a housing for at least two different cartridges (2, 2′). The invention is characterized in that said pocket (29) comprises a single peripheral seat (35) common to several cartridges (2, 2′) of different seat diameters, one or more portions of the outer rim of said peripheral seat 835) forming an indexing vertical wall common to said cartridges (2, 2′).