The Lifshits method of local perturbations is used for studying the properties of a two-dimensional electron-impurity system in a quantizing magnetic field perpendicular to the plane of electron motion. The high-frequency conductivity tensor of the system is calculated in the model of independent point impurity atoms, taking into account the impurity states of electrons and spatial dispersion. The dissipative component of the conductivity has narrow resonant peaks at frequencies of electron transitions between the Landau levels and local levels, which are induced by the magnetic field. In zero magnetic field, these peaks merge into one broad peak lying above the threshold frequency for electron transitions from a local level to the energy band. Numerical values of the peak heights are obtained for semiconducting structures with a two-dimensional electron gas. ©1997 American Institute of Physics.