A general analysis has been given in part I of symmetric elastic surface waves, characterized by the coincidence of the reference plane with a plane of material symmetry. There follows here a detailed account of the propagation of such waves in media with monoclinic, the minimum type of symmetry. The three definite integrals involved in the determination of the surface-wave function, and hence the speed of propagation, are evaluated and an explicit formula is obtained connecting a fourth integral, also required in the calculation of surface-wave properties, to the other three. Illustrative numerical results are presented, referring in all to 12 monoclinic crystals. The continuous transitions between subsonic and supersonic surface-wave propagation, encountered previously in cubic and transversely isotropic elastic media, occur in seven of the materials and thus emerge as a customary feature of symmetric surface waves. Computations of the associated displacement and traction fields and the paths of particles in the boundary of the transmitting body are also described.