  A non-relativistic classification of charged molecular hydrogenic, helium and
mixed helium-hydrogenic chains with one or two electrons which can exist in a
strong magnetic field $B \lesssim 10^{16} $G is given. It is shown that for
both $1e-2e$ cases at the strongest studied magnetic fields the longest
hydrogenic chain contains at most five protons indicating to the existence of
the $\rm{H}_5^{4+}$ and $\rm{H}_5^{3+}$ ions, respectively. In the case of the
helium chains the longest chains can exist at the strongest studied magnetic
fields with three and four $\al-$particles for $1e-2e$ cases, respectively. For
mixed helium-hydrogenic chains the number of heavy centers can reach five for
highest magnetic fields studied. In general, for a fixed magnetic field
two-electron chains are more bound than one-electron ones.
