An analysis of the modes that can propagate in a parallel-plate waveguide with lossless reactive guiding surfaces is presented. Three cases are considered: (1) where both surfaces are inductive, (2) where both surfaces are capacitive, and (3) where one of the surfaces is inductive and the other is capacitive. In general, we found two surface waves and an infinite number of waveguide modes. Although all the waveguide modes exhibit the cutoff phenomenon, the surface wave modes may either propagate down to zero frequency or may be critical. At certain ‘threshold’ frequencies, a transition is observed from one to the other type of mode.