Compressional Pc 3 magnetic pulsations with large wave numbers normal to the static magnetic field in the magnetosphere and the beating type Pc 3 pulsations on the ground are hardly interpreted with respect to the linear resonance theory based on the idea of a resonance coupling between a monochromatic surface wave at the magnetopause and a shear Alfv¿n wave at a local field line in the inner magnetosphere. A parametric excitation of an Alfv¿n wave (kA, &ohgr;A) by a magnetosonic pump wave (k fs1, &ohgr;1fs), which propagates obliquely to the static magnetic field, has been analyzed. The resonance conditions are chosen such that k fs1 =k fs2+kA and &ohgr;1fs-&ohgr;A=Δ~&ohgr;2fs. For both standing and propagating pumps the growth rates of the excited HM waves depend not only on the pump power but also on &bgr;. It is found that large growth rates of parametric excitation of Alfv¿n waves by the fast magnetosonic pump waves arise if &thgr;1f=~(k f1, B0) ~70¿--80¿ and the regions of parametric excitation are localized at the resonance point in the magnetosphere where &bgr;~me/mi. It is concluded that parametric excitation of Pc 3 range HM waves is a more attractive theory of the beating type geomagnetic pulsations than the linear resonance theory.