his thesis presents the investigations and the interpretation of long quasi-periodic oscillations with periods more than 30 minutes observed in the magnetic field of sunspots, as well as, at millimeter radio emission nearby sunspots. Additionally, the same phenomenon of long quasi-periodic oscillations was studied for the magnetic field of smallscale magnetic structures related to the facular knots observed in solar chromosphere. Two different methods of data processing are used to obtain the quasi-periodicity. The first method is the traditional Wavelet transform, and the second method is the Empirical Mode Decomposition (EMD).

Firstly, long quasi-periodic oscillations of the millimeter (37 GHz) radio emission of active regions above sunspots were obtained with periods in the interval of 1-5 hours. The same periods were obtained for the magnetic field of the sunspots observed in these active regions. The time-lags between the magnetic field oscillations and the millimeter radio emission oscillations were derived in the interval of 15-30 minutes. The interpretation of observed oscillations and lags was done by using the so-called "three-fluxes" model. Secondly, the non-stationary long quasi-periodic oscillations of the magnetic field of facular knots were obtained with periods in the interval of 30-260 minutes. The interpretation of the observed periodicities was done by using the modelling of oscillations of the system with a time-varying rigidity.

Three-fluxes model together with the shallow sunspot model gave the physical interpretation of the observed long quasi-periodic oscillations of the millimeter radio emission and the magnetic field of sunspots. Hydrostatic rebuilding of physical parameters of millimeter radio source modulated by the oscillations of the magnetic field of a sunspot as a whole describes the observed lags between the time series in the interval of 15-30 minutes, when the radio emission delay relatively to the magnetic field variations. In the other case, the shallow sunspot model could not be directly used to provide the interpretation of the observed oscillations of facular knots. This requires a number of physical parameters, that have not been observed yet (the analog ofWilson’s depression of the sunspot, the lower boundary of the facular knot). In this case, the model of the facular knot as the system with the time-varying rigidity is in good agreement with the observed dynamics of these objects, and it could be the first step to the new analytical model of the facular knot that will consider the dynamical properties of this small-scale object.