A method is described for the construction of a density wave of finite amplitude and in the form of a tightly wound spiral in a pressureless, self-gravitating disk of infinitesimal thickness in an external gravitational field. Waves of one kind are found for systems in which the law of rotation departs only slightly from that of a solid body. Waves of a second kind are found in systems possessing appreciable differential rotation; however, such waves can occur only if the self-gravitation of the disk is small compared with the external gravitation. The latter waves are to be identified with the waves described by linear theories.