  A microscopic few-body description of near-threshold coherent photoproduction
of the eta-meson on tritium and He3 targets is given. The photoproduction
cross-section is calculated using the Finite Rank Approximation (FRA) of the
nuclear Hamiltonian. The results indicate a strong final state interaction of
the eta-meson with the residual nucleus. Sensitivity of the results to the
choice of the eta-N T-matrix is investigated. The importance of obeying the
two-body unitarity condition in the eta-N system is demonstrated.
