  Radiative shock waves may be subject to a global thermal instability in which
the cooling layer and shock front undergo growing resonant oscillations. For
strong hydrodynamic shocks, the presence of the overstability depends on the
temperature and density indices of power-law cooling functions and the specific
heat ratio, $\alpha$, $\beta$ and $\gamma$, respectively. Here, we investigate
the stabilising influence of a transverse magnetic field by introducing the
shock Alfv\'en number, $M_a$ as a fourth parameter. We thus investigate the
stability criteria for both molecular and atomic shocks under a wide range of
conditions. In particular, we find that all molecular shocks in which the
cooling increases with the temperature ($\alpha > 0$) are stabilised to the
first four modes if $M_a < 20$ ($\beta = 2$). For $\alpha = -0.5$, the first
overtone remains stable only for $M_a < 8$. We conclude that molecular shocks
in the interstellar medium are probably stabilised by a transverse magnetic
field unless exceptional circumstances arise in which the cooling strongly
increases as the gas cools.
