The response of the magnetosphere boundary in a steady solar wind to small initial departures from equilibrium is investigated in accordance with the classical model of Chapman and Ferraro. If the wavelength and amplitude are sufficiently small that curvature and second-order effects can be disregarded, all perturbations, except those having wave fronts aligned with the direction of the local magnetic field, are found to damp exponentially with time and to drift along the boundary with the tangential component of the solar wind. Aligned waves, which neither damp nor amplify in this approximation, are examined further by inclusion of curvature and higher order effects. A first-order analysis shows that curvature introduces a destabilizing effect in small regions in the vicinity of the neutral points and a stabilizing effect elsewhere. Possible geophysical consequences, such as the persistent magnetic agitation of the polar regions, are discussed. An exact solution for an aligned cylindrical solitary wave having an initial form of a circular arc is also presented to illustrate a mode of response that appears to permit injection of elongated and widely separated columns of solar wind plasma into the magnetosphere under certain conditions and to provide a mechanism for momentum transfer from the solar wind to the ambient magnetosphere plasma.