  Unstable states of the eta meson and the 3He nucleus predicted using the time
delay method were found to be in agreement with a recent claim of eta-mesic 3He
states made by the TAPS collaboration. Here, we extend this method to a
speculative study of the unstable states occurring in the eta-d and eta-4He
elastic scattering. The T-matrix for eta-4He scattering is evaluated within the
Finite Rank Approximation (FRA) of few body equations. For the evaluation of
time delay in the eta-d case, we use a parameterization of an existing Faddeev
calculation and compare the results with those obtained from FRA. With an eta-N
scattering length, $a_{\eta N} = (0.42, 0.34)$ fm, we find an eta-d unstable
bound state around -16 MeV, within the Faddeev calculation. A similar state
within the FRA is found for a low value of $a_{\eta N}$, namely, $a_{\eta N} =
(0.28, 0.19)$ fm. The existence of an eta-4He unstable bound state close to
threshold is hinted by $a_{\eta N} = (0.28, 0.19)$ fm, but is ruled out by
large scattering lengths.
