The NUCLEON experiment was designed to study the chemical composition and energy spectra of galactic cosmic ray nuclei from protons to zinc at energies of $sim10^{11}$--$10^{15}$,eV per particle. The research was carried out with the NUCLEON scientific equipment installed on the Russian satellite Resurs-P No.,2 as an additional payload. This article presents the results for the measured nuclei spectra related to the first approximately 250 days of the scientific data collection during 2015 and 2016. The all-particle spectrum and the spectra of p, He, C, O, Ne, Mg, Si and Fe are presented. Some interesting ratios of the spectra are also presented and discussed. The experiment is now in its beginning stage and the data still have a preliminary character, but they already give numerous indications of the existence of various non-canonical phenomena in the physics of cosmic rays, which are expressed in the violation of a simple universal power law of the energy spectra. These features of the the data are briefly discussed.