The response of a coastal current forced by a steady wind stress over a sloping continental shelf is investigated. A Laplace transform technique is used, and it is shown that in the adjustment to a steady state the response consists of a damped, propagating disturbance, carrying energy offshore and longshore. This may be associated with shelf waves, but the response is not related to any poles of the image function. The spectrum is continuous, and a discrete set of 'normal modes' does not exist.