Rotary filling machine, comprising: • a rotating infeed starwheel configured to supply packages; • a rotating filling carrousel upon which a plurality of filling stations are arranged diametrically to the same, each one of which is configured to receive a package coming from the infeed starwheel, wherein each filling station comprises: • dosage means, configured to administer the dosage of a product inside the package; • vertical displacement means configured to vary the relative distance between the package and the dosage means in the direction of a vertical axis and; • rotation means, configured to provide a relative rotation movement between the package and the dosage means, around the vertical axis, wherein the rotation means are configured to rotate the package in relation to the carrousel; and • a rotating outfeed starwheel, configured to remove the packages from the filling carrousel, wherein both infeed and outfeed starwheels are configured to rotate in synchronisation with the filling carrousel; said machine being characterised in that each filling station comprises: • horizontal displacement means, configured to vary the relative distance between the package and the dosage means on a horizontal plane perpendicular to the vertical axis; and in that the rotation means comprise: • a vertical bar joined to the carrousel, which is coaxial to the vertical axis and has freedom of axial rotation; • a rotation base arranged on an upper end of the vertical bar, configured to receive a package coming from the infeed starwheel and; • a rotation mechanism, configured to rotate the vertical bar. • a rotating infeed starwheel configured to supply packages; • a rotating filling carrousel upon which a plurality of filling stations are arranged diametrically to the same, each one of which is configured to receive a package coming from the infeed starwheel, wherein each filling station comprises: • dosage means, configured to administer the dosage of a product inside the package; • vertical displacement means configured to vary the relative distance between the package and the dosage means in the direction of a vertical axis and; • rotation means, configured to provide a relative rotation movement between the package and the dosage means, around the vertical axis, wherein the rotation means are configured to rotate the package in relation to the carrousel; and • dosage means, configured to administer the dosage of a product inside the package; • vertical displacement means configured to vary the relative distance between the package and the dosage means in the direction of a vertical axis and; • rotation means, configured to provide a relative rotation movement between the package and the dosage means, around the vertical axis, wherein the rotation means are configured to rotate the package in relation to the carrousel; and • a rotating outfeed starwheel, configured to remove the packages from the filling carrousel, wherein both infeed and outfeed starwheels are configured to rotate in synchronisation with the filling carrousel; said machine being characterised in that each filling station comprises: • horizontal displacement means, configured to vary the relative distance between the package and the dosage means on a horizontal plane perpendicular to the vertical axis; • a vertical bar joined to the carrousel, which is coaxial to the vertical axis and has freedom of axial rotation; • a rotation base arranged on an upper end of the vertical bar, configured to receive a package coming from the infeed starwheel and; • a rotation mechanism, configured to rotate the vertical bar.