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 Alfvén 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 .