  We calculate the Compton and annihilation production of a soft static lepton
pair in a quark-gluon plasma in the two-loop approximation. We work in the
context of the effective perturbative expansion based on the resummation of
hard thermal loops. Double counting is avoided by subtracting appropriate
counterterms. It is found that the two-loop diagrams give contributions of the
same order as the one-loop diagram. Furthermore, these contributions are
necessary to obtain agreement with the naive perturbative expansion in the
limit of vanishing thermal masses.
