We analyse the oxygen abundance and specific star formation rates (sSFR) variations with redshift in star-forming Sloan Digital Sky Survey (SDSS) galaxies of different masses. We find that the maximum value of the sSFR, sSFRmax, decreases when the stellar mass, MS, of a galaxy increases and decreases with decreasing of redshift. The sSFRmax can exceed the time averaged sSFR by about an order of magnitude for massive galaxies. The metallicity-redshift relations for subsamples of galaxies with sSFR = sSFRmax and with sSFR = 0.1 × sSFRmax coincide for massive [log(MS/M⊙) ≳ 10.5, with stellar mass MS in solar units] galaxies and differ for low-mass galaxies. This suggests that there is no correlation between oxygen abundance and sSFR in massive galaxies and that the oxygen abundance correlates with the sSFR in low-mass galaxies. We find evidence in favour of that the irregular galaxies show, on average, higher sSFR and lower oxygen abundances than the spiral galaxies of similar masses and that the mass-metallicity relation for spiral galaxies differsslightly from that for irregular galaxies. The fact that our sample of low-mass galaxies is the mixture of spiral and irregular galaxies can be responsible for the dependence of the metallicity-redshift relation on the sSFR observed for the low-mass SDSS galaxies. The mass-metallicity and luminosity-metallicity relations obtained for irregular SDSS galaxies agree with corresponding relations for nearby irregular galaxies with direct abundance determinations. We find that the aperture effect does not make a significant contribution to the redshift variation of oxygen abundances in SDSS galaxies.