Abstract: The flapping stop device of the invention is intended for a gyroplane rotor comprising a hub (3) to which each blade (22) is connected by retaining and pivoting members (16) having two frames, one (17) of which is fixed to the hub (3) and the other (19) of which, in an internal radial position with respect to the first one, is locked for movement with the root (23) of the blade (22). The internal frame (19) has, projecting radially inwardly, at least one nose piece (29) having a stop surface and defining a convex cylindrical sliding surface (28) on the internal radial face of the frame (19). The nose piece or pieces (29) and the convex surface (28) cooperate respectively with one or more bearing surfaces (34) and a complementary concave surface (33) of a central stop (30) integral with the hub (3) or with the rotor mast (2).