  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.
