  We study the divergence of large-order perturbation theory in the worldline
expression for the two-loop Euler-Heisenberg QED effective Lagrangian in a
constant magnetic field. The leading rate of divergence is identical, up to an
overall factor, to that of the one-loop case. From this we deduce, using Borel
summation techniques, that the leading behaviour of the imaginary part of the
two-loop effective Lagrangian for a constant E field, giving the
pair-production rate, is proportional to the one-loop result. This also serves
as a test of the mass renormalization, and confirms the earlier analysis by
Ritus.
