  We consider the hydrogen molecular ion $H^+_2$ in the presence of a strong
homogeneous magnetic field. In this regime, the effective Hamiltonian is almost
one dimensional with a potential energy which looks like a sum of two Dirac
delta functions. This model is solvable, but not close enough to our exact
Hamiltonian for relevant strenght of the magnnetic field. However we show that
the correct values of the equilibrium distance as well as the binding energy of
the ground state of the ion, can be obtained when incorporating perturbative
corrections up to second order. Finally, we show that $ He_2^{3+}$ exists for
sufficiently large magnetic fields.
