We investigate the problem of stellar pulsation in the presence of a magnetic field, for arbitrary frequencies and horizontal wavenumbers. Magnetic effects are strong in a boundary layer close to the stellar surface, but it is possible to identify independent Alfvénic-type modes at sufficient stellar depth. We show how the boundary layer solutions can be matched to the interior solutions for a range of horizontal wavenumbers, this range increasing with frequency. We calculate the energy flux carried by the Alfvénic modes and show that the loss of pulsational energy via these waves is significant, this being especially so for high horizontal wavenumbers. Our results are of particular interest to observations of pulsating magnetic Ap stars.