The plasma model for the magnetosphere and ionosphere is first discussed. A review of some parts of the theory for a warm collisionless plasma of interest in the magnetosphere in connection with waves of periods between 0.1 and 1000 seconds is given. The theory for magnetohydrodynamic waves in a slightly ionized gas is then summarized. The available observational data about magnetospheric and ionospheric phenomena, which may be interpreted in terms of waves with periods between 0.1 and 1000 seconds, are briefly surveyed and some theoretical applications to the ionosphere and magnetosphere are finally discussed. The theory of shock phenomena and transients in the magnetosphere is not included in the report.