  The main goal of this work is to calculate the contributions to the
cosmological recombination spectrum due to bound-bound transitions of helium.
We show that due to the presence of helium in the early Universe unique
features appear in the total cosmological recombination spectrum. These may
provide a unique observational possibility to determine the relative abundance
of primordial helium, well before the formation of first stars. We include the
effect of the tiny fraction of neutral hydrogen atoms on the dynamics of HeII
-> HeI recombination at redshifts $z\sim 2500$. As discussed recently, this
process significantly accelerates HeII -> HeI recombination, resulting in
rather narrow and distinct features in the associated recombination spectrum.
In addition this process induces some emission within the hydrogen
Lyman-$\alpha$ line, before the actual epoch of hydrogen recombination round
$z\sim 1100-1500$. We also show that some of the fine structure transitions of
neutral helium appear in absorption, again leaving unique traces in the Cosmic
Microwave Background blackbody spectrum, which may allow to confirm our
understanding of the early Universe and detailed atomic physics.
