REBa2Fe3O8+wphases (RE=Dy, Er, and Y) with a varied oxygen content (-0.25<w<0.10 in general, widest forRE=Dy, narrowest forRE=Er) have been obtained by quenching from controlled atmospheres. The triple-perovskite-type structure is adopted for these phases, with two crystallographically different iron atoms, tetragonal abovew≈-0.15 and orthorhombic below that oxygen content. The valence and spin states of iron are investigated using57Fe Mössbauer spectroscopy. At room temperature, an antiferromagnetic ordering is observed for all values ofw. Six- and five-coordinated Fe3+,S=52environments are distinguished in the Mössbauer spectra and their occupancies forw=0 are in the exact structural ratio of these two coordinations. Forw>0, tetravalent iron (S=2) accompanies the extra oxygen atoms at the (originally) square-pyramidal Fe site, whereas divalent iron (S=2) accompanies the oxygen vacancies formed in the octahedral Fe site whenw<0. The latter splits into two components, the intensities of which correspond to the fractions of five- and four-coordinated iron with a random distribution of meridial oxygen vacancies in an octahedron.