Experiments carried out with a rotating model basin confirm the existence of a type of slow oscillation (double Kelvin wave) predicted by linearized shallow-water theory. Such oscillations may occur in the neighbourhood of any zone where a bottom slope separates two regions of uniform depth. The energy is propagated along the contours of constant depth, with the shallower water always to the right of the direction of propagation (in the northern hemisphere). The theoretical dispersion relation is well verified, including the existence of a maximum frequency, and consequently a vanishing group-velocity, at a certain wavenumber. When the wavemaker is operated at a frequency greater than this maximum, steady currents are sometimes generated. The effects of curvature of the bottom contours are discussed, as well as the loss of energy by viscous dissipation in the bottom boundary-layer.