  The cross section for the reaction $dd\rightarrow \,^4\!H\!e\,\eta$ close to
threshold is estimated in a two-step model, similar to that which successfully
describes near-threshold $pd\rightarrow \,^3\!H\!e\,\eta$ production. A
$\pi$-meson, created in a $dp\rightarrow \,^3\!H\!e\,\pi^o$ process on one
nucleon in the target deuteron, is converted into an $\eta$-meson by a
secondary $\pi^o n \to n\,\eta$ reaction on the other nucleon. The kinematics
are such that both processes are nearly physical so that only small Fermi
momenta are required. The predictions of the model are in good agreement with
recent Saclay experimental data.
  An analogous model, when applied to the near-threshold
$n\,^3\!H\!e\rightarrow \,^4\!H\!e\,\eta$ reaction, predicts a cross section of
a rather similar size, but experimental difficulties render this a doubtful
means of studying the $\eta\, ^4\!H\!e$ interaction.
