  Accurate calculations for the ground state of the molecular ions He$_2^{3+}$
and HeH$^{2+}$ placed in a strong magnetic field $B\gtrsim 10^{2}$ a.u.
($\approx 2.35 \times 10^{11}$G) using the Lagrange-mesh method are presented.
The Born-Oppenheimer approximation of zero order (infinitely massive centers)
and the parallel configuration (molecular axis parallel to the magnetic field)
are considered. Total energies are found with 9-10 s.d. The obtained results
show that the molecular ions He$_2^{3+}$ and HeH$^{2+}$ exist at $B >
100$\,a.u. and $B > 1000$\,a.u., respectively, as predicted in \cite{Tu:2007}
while a saddle point in the potential curve appears for the first time at $B
\sim 80$ a.u. and $B \sim 740$ a.u., respectively.
