Hydromagnetic waves in the magnetosphere are affected by the presence of the adjacent conducting ionosphere and insulating atmosphere. Boundary conditions at the ionosphere are derived under the assumption that the magnetospheric wavelength is much larger than the height of the ionosphere or atmosphere. Unlike earlier works, our boundary conditions are expressed in a form that applies both to pure Alfven or magnetosonic waves and to fully coupled waves. The use of these new conditions is demonstrated by giving an exact solution, within the box model, to a special case of excitation of magnetospheric micropulsations. It is shown that, consistent with well-known observations, the amplitude of resonantly excited micropulsations is much larger in the dayside magnetosphere than in the nightside because of the larger dayside ionospheric conductivity. We argue that the efficiency of wave damping by the low-conductivity nightside ionosphere is not a convincing explanation of this phenomenon. Our alternative interpretation is that the Alfven resonances are not efficiently excited where the ionsopheric conductivity is low because boundary conditions impose different field-aligned structure on the compressional and transverse parts of a signal. The differences diminish as the conductivity increases, allowing resonant coupling to become efficient. ¿ American Geophysical Union 1991