  The Coulombic systems $(\al p e)$ and $(\al\al e)$, $(\al p p e)$,
  $(\al \al p e)$ and $(Li^{3+} Li^{3+} e)$ placed in a magnetic field $B
\gtrsim 10^{11} {G}$ are studied. It is demonstrated a theoretical existence of
the exotic ion $(He H)^{2+}$ for $B\gtrsim 5\times 10^{12} {G}$ in parallel
configuration (the magnetic field is directed along internuclear axis) as
optimal as well as its excited states $1\pi, 1\delta$. As for the exotic ion
${He}_{2}^{3+}$ it is shown that in spite of strong electrostatic repulsion of
$\al-$particles this ion can also exist for $B \gtrsim 100 {a.u.} (= 2.35\times
10^{11} {G})$ in parallel configuration as optimal in the states $1\si_g$
(ground state), $1\pi_u, 1\delta_g$. Upon appearance both ions are unstable
towards dissociation with $He^+$ in the final state but with very large
lifetime. However, at $B\gtrsim 10000$ a.u. the ion $(He H)^{2+}$ becomes
stable, while at $B\gtrsim 1000$ a.u. the ion ${He}_{2}^{3+}$ becomes stable.
With a magnetic field growth, both exotic ions become more and more tightly
bound and compact, their lowest rotational and vibrational energies grow. At
the edge of applicability of non-relativistic approximation, $B \sim 4.414
\times 10^{13}$ G, there are indications that three more exotic linear ions
$(H-He-H)^{3+}$, $(He-H-He)^{4+}$ and even $Li_2^{5+}$ in parallel
configuration may also occur.
