  Extending our earlier treatments of pi0, eta_c and eta_b, we study the
eta-eta' system and its gamma-gamma decays using a model which is a leading
version of the consistently coupled Schwinger-Dyson (SD) and Bethe-Salpeter
(BS) approach. The electromagnetic interactions are incorporated through a
(generalized) impulse approximation consistent with this bound-state approach,
so that the Ward-Takahashi identities of QED are preserved when quarks are
dynamically dressed. To overcome some of the limitations due to the ladder
approximation, we introduce a minimal extension to the bound--state approach
employed, so that the U_A(1) problem is avoided. Pointing out which of our
predictions hold in the coupled SD-BS approach in general, and which are the
consequences of the specific, chosen model, we present the results for the
axial-current decay constants of eta_8, eta_0, and of their physical
combinations eta and eta', the results for the gamma-gamma decay constants of
eta_0 and eta_8, for the two-photon decay widths of eta and eta', and for the
mixing-independent R-ratio constructed from them.
