In the framework of the study of the evolutionary status of galaxies in the nearby Lynx-Cancer void, we present the results of the SAO RAS 6-m telescope spectroscopy for 20 objects in this region. The principal faint line [OIII]4363A, used to determine the electron temperature and oxygen abundance (O/H) by the classical method, is clearly detected in only about 2/3 of the studied objects. For the remaining galaxies this line is either faint or undetected. To obtain the oxygen abundances in these galaxies we as well apply the semi-empirical method by Izotov and Thuan, and/or the empirical methods of Pilyugin et al., which are only employing the intensities of sufficiently strong lines. We also present our O/H measurements for 22 Lynx-Cancer void galaxies, for which the suitable Sloan Digital Sky Survey (SDSS) spectra are available. In total, we present the combined O/H data for 48 Lynx-Cancer void galaxies, including the data adopted from the literature and our own earlier results. We make a comparison of their locations on the (O/H)-M_B diagram with those of the dwarf galaxies of the Local Volume in the regions with denser environment. We infer that the majority of galaxies from this void on the average reveal an about 30% lower metallicity. In addition, a substantial fraction (not less than 10%) of the void dwarf galaxies have a much larger O/H deficiency (up to a factor of 5). Most of them belong to the tiny group of objects with the gas metallicity Z < Zo/20 or 12+log(O/H) <~7.35. The surface density of very metal-poor galaxies (Z < Zo/10} in this region of the sky is 2--2.5 times higher than that, derived from the emission-line galaxy samples in the Hamburg-SAO and the SDSS surveys. We discuss possible implications of these results for the galaxy evolution models.
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