The geometrical and electronic structures of the Cr2On and Cr2On- clusters are computed using density functional theory with a generalized gradient approximation in the range of 1 <= n <= 14. Local total spin magnetic moments, polarizabilities, binding energies per atom, and energies of abstraction of O and O-2 are computed for both series along with electron affinities of the neutrals and vertical detachment energies of the anions. In the lowest total energies states of Cr2O2, Cr2O3, Cr2O4, Cr2O14, Cr2O3-, Cr2O4-, and Cr2O14-, total spin magnetic moments of the Cr atoms are quite large and antiferromagnetically coupled. In the rest of the series, at least one of the Cr atoms has no spin-magnetic moment at all. The computed vertical electron-detachment energies of the Cr2On- are in good agreement with experimental values obtained in the 1 <= n <= 7 range. All neutral Cr2On possess electron affinities larger than the electron affinities of halogen atoms when n > 6 and are thus superhalogens. It is found that the neutrals and anions are stable with respect to the abstraction of an O atom in the whole range of n considered, whereas both neutrals and anions became unstable toward the loss of O-2 for n > 7. The polarizability per atom decreases sharply when n moves from one to four and then remains nearly constant for larger n values in both series. The largest members in both series, Cr2O14 and Cr2O14-, possess the geometrical structures of the Cr-2(O-2)(7) type by analogy with monochromium Cr(O-2)(4).