The coupling of compressional and Alfv¿n modes is important in solar, magnetospheric, and laboratory plasmas. We investigate such coupling within a general framework, but concentrate upon applying our results to the excitation of Alfv¿n waves in the magnetosphere. The Alfv¿nic response of an arbitrary (curl-free) magnetic field and ideal cold plasma is considered, and the Alfv¿n wave equation is shown to be driven by perturbation magnetic pressure gradients aligned with the Alfv¿n fields. The efficiency with which any particular standing Alfv¿n wave is excited is governed by an overlap integral along the background field line of the Alfv¿n mode and the perturbation magnetic pressure gradient. Three types of compressional driving function are investigated which produce diverse behavior and may excite resonant and nonresonant Alfv¿n waves. These waves oscillate with either the natural Alfv¿n frequency or the frequency of the driver. Finally we turn our attention to the long-term, or asymptotic, state of the fields. A nonlinear solution is derived which is a generalization of earlier work. We find that the standing Alfv¿n waves will be confined to thin layers. ¿ American Geophysical Union 1992