A cigarette packaging machine provided with a wrapping wheel to wrap products in wrapping sheets. The wrapping wheel has peripheral pockets to receive the products and the wrapping sheets, a first loading station to load the products in succession into the peripheral pockets, and a second loading station to load, in succession, first wrapping sheets of the wrapping sheets into the peripheral pockets. The wrapping wheel also has a third loading station to load, in succession, second wrapping sheets of the wrapping sheets into the peripheral pockets, thus reducing the bulk of a packaging machine.