  Ab initio method based on a complex-scaling approach and aimed at a rigorous
QED description of autoionizing states is worked out. The autoionizing-state
binding energies are treated nonperturbatively in $\alpha Z$ and include all
the many-electron QED contributions up to the second order. The higher-order
electron correlation, nuclear recoil, and nuclear polarization effects are
taken into account as well. The developed formalism is demonstrated on the $LL$
resonances in heliumlike argon and uranium. The most accurate theoretical
predictions for the binding energies are obtained.
