A nasal delivery device for a powder, having a reservoir, a delivery head and an air discharge system generating a flow of compressed air. The air discharge system has an air chamber, formed by a hollow axial cylinder, and a piston that sealingly slides in the air chamber to compress the air. The hollow axial cylinder has a radial shoulder connecting a first cylinder portion and a second cylinder portion. Before actuation, the piston is at the first cylinder portions and, during actuation, the piston sealingly cooperates with the second cylinder portion. The radial shoulder defines a profile that the piston overcomes at start of actuation. The piston has an upper lip and a lower lip, a skirt around the hollow axial cylinder with a lower flange projecting radially inward. The skirt has a profile radially projecting towards the inside, cooperating before actuation with the lower lip of the piston.