A pure surface wave requires, in principle, unbounded space outside the supporting surface, thus permitting the field in the transverse plane to decay, without obstruction, to zero at an infinite distance from the surface. Such a wave cannot therefore be contained within a screen, unless the bounding surface matches precisely the field impedance at the point of its location. A surface of this kind must have capacitive reactance and a small negative resistance, which implies a subsidiary generator. A second surface wave, supported on the inside of the screen, can be set up to satisfy the boundary conditions, and the paper discusses arrangements that should meet the requirements, enabling full or partial screening to be achieved. Moreover it appears that the dual surface wave proposed may have a lower attenuation in a straight guide than the corresponding TEM mode.