A packaging apparatus for nappies or other soft, flat, folded sanitary articles, comprising: - packaging means for positioning a plastic film so it is tight against a set of nappies, wherein the set of nappies comprises one or more groups of nappies that are superposed in such a way that the different groups of nappies are in contact with each other along the lateral edges, wherein each group of nappies comprises a plurality of nappies that are juxtaposed with each other in such a way that each nappy has at least one of its two flat faces facing a corresponding face of an adjacent nappy; - a feeder set up to feed the nappies to the packaging means; wherein the packaging means comprise a wrapping machine configured to fold a sheet of the film round the set of nappies and to close it on at least three sides of the set of nappies, wherein the wrapping machine includes an infeed station, having a downwardly directed opening for receiving the set of nappies, and a first and a second carriage, which have two walls for laterally retaining the set of nappies and are movable relative to each other to compress a set of nappies which is held by them; - a presser operatively coupled to the feeder and configured to laterally press the groups of juxtaposed nappies from the sides, on the flat lateral faces of the groups of nappies to compress them, characterized in that the apparatus comprises: - at least one comb configured to selectively withdraw groups of nappies from a nappy stacker device and place them on the feeder, - a programmable control unit, wherein the presser is controlled by said programmable control unit, to compress the groups of nappies until reaching a lateral dimension having a predetermined reference value smaller than a width defined by said infeed station of the wrapping machine, and wherein the wrapping machine comprises actuators connected to the control unit for moving the carriages, the control unit being programmed to apply compression to the set of nappies closed on said at least three sides of the set of nappies, before a fourth side is closed, wherein the control unit is configured to drive the actuators to move the carriages relative to each other, for further compressing the set of nappies. - packaging means for positioning a plastic film so it is tight against a set of nappies, wherein the set of nappies comprises one or more groups of nappies that are superposed in such a way that the different groups of nappies are in contact with each other along the lateral edges, wherein each group of nappies comprises a plurality of nappies that are juxtaposed with each other in such a way that each nappy has at least one of its two flat faces facing a corresponding face of an adjacent nappy; - a feeder set up to feed the nappies to the packaging means; - a presser operatively coupled to the feeder and configured to laterally press the groups of juxtaposed nappies from the sides, on the flat lateral faces of the groups of nappies to compress them, characterized in that the apparatus comprises: - at least one comb configured to selectively withdraw groups of nappies from a nappy stacker device and place them on the feeder, - a programmable control unit, wherein the presser is controlled by said programmable control unit, to compress the groups of nappies until reaching a lateral dimension having a predetermined reference value smaller than a width defined by said infeed station of the wrapping machine,