Аннотация:Kappa functions describe particle distributions for the systems that are in stationary state but out of thermal equilibrium. The form of the kappa distribution consists of a Maxwellian core at low energies and a power law spectrum at high energies. Simultaneous determination of the parameters of kappa distributions in different space regions is important for understanding the role of different processes of particle acceleration and relaxation of kappa distribution functions to the Maxwellian ones. We study kappa distributions in different magnetospheric regions and magnetosheath, using the data of the Time History of Events and Macroscale Interactions during Substorms (THEMIS) mission. Problems of obtaining kappa approximations are connected with different sensitivity of devices measured particle fluxes in different energy ranges and pitch angles. Another difficulty is connected with frequently observed mixtures of plasmas of different origins. It was found, that in the regions, where distribution functions are formed due to mixing of two plasma populations, they can be described using bi-kappa distributions. Such feature permits to select the contribution of every plasma population in the whole one. We show that analyzing the space distribution of k-parameter it is possible to determine the location of the region of acceleration for a specific particle population. We try to evaluate the characteristic times of distribution function relaxation by analyzing measurements during different phases of auroral substorm.