Abstract. A theory of resonant conversion of fast magnetosonic (FMS) waves into slow magnetosonic (SMS) oscillations in a magnetosphere with dipole-like magnetic field has been constructed. Monochromatic FMS waves are shown to drive standing (along magnetic field lines) SMS oscillations, narrowly localized across magnetic shells. The longitudinal and transverse structures, as well as spectrum of resonant SMS waves are determined. Frequencies of fundamental harmonics of standing SMS waves lie in the range of 0.1–1 mHz, and are about two orders of magnitude lower than frequencies of similar Alfvén field line resonance harmonics. This difference makes an effective interaction between these MHD modes impossible. The amplitude of SMS oscillations rapidly decreases along the field lines from the magnetospheric equator towards the ionosphere. In this context, magnetospheric SMS oscillations cannot be observed on the ground, and the ionosphere does not play any role either in their generation or dissipation. The theory developed can be used to interpret the occurrence of compressional Pc5 waves in a quiet magnetosphere with a weak ring current.