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We analyze the simultaneous observations of the fluxes of auroral electrons and the fluxes of relativistic electrons at the external boundary of the outer electron radiation belts using data of METEOR-M No1 satellite for the period from November 3, 2009 till April 30, 2010. The geomagnetic conditions during analyzed period were comparatively quite. METEOR-M №1 has a polar solar-synchronous circular orbit with an altitude of ~832 km, a period of 101.3 min, and an inclination of 98.068 degrees. The electrons with the energies from 0.1 to 13 MeV and protons from 1 to 260 MeV were measured by GGAK-M instrument composed by semiconductor and scintillator detectors. The plasma electrons with the energies from 0.03 to 16 keV were measured by the segment electrostatic analyzer. The observation of fluxes of relativistic electrons were selected inside the auroral oval connected with the development of magnetospheric substorms. However, the fluxes of relativistic electrons are also observed during absolutely quite time intervals. We compare the obtained results with the observations of CORONAS-FOTON satellite demonstrating the quasistationary (for more than 3 hours) increases of relativistic electrons at the latitudes of the auroral oval and argue that the processes inside the auroral oval can play the considerable role in the acceleration of relativistic electrons