  An estimate is made of the Landau-Pomeranchuk effect on the production of
dileptons in a hadronic gas and in a quark-gluon plasma. For low mass dilepton
pairs this effect reduces the production rate for bremsstrahlung by an order of
magnitude. For high invariant masses its influence is negligible. This
behaviour is of importance for the theoretical analysis of low mass dilepton
pairs produced in relativistic heavy ion collisions.
