The coupling of compressional and transverse hydromagnetic waves is studied in the cold and inhomogeneous outer magnetosphere. A general computer program has been developed for a dipole model. This model allows a realistic spatial variation of Alfven speed and includes dipole geometric effects. The propagation and the structure of each mode are analyzed on a two-dimensional map of a meridian plane. The properties of coupling are also investigated through time histories and wave frequency spectra. The highly spatially structured form of transverse and compressional waves is shown on the meridian plane. The theory of global compression mode damping is compared with the numerical results. We have found a set of global modes whose spatial structure is complicated due to the inhomogeneity of the dipole geometry. These global modes are strongly coupled to field line resonances when the global mode frequency is harmonically matched to the toroidal resonant frequency. The coupling of the two modes results in relatively large-amplitude oscillations along the resonant field lines. ¿ American Geophysical Union 1989