Core-melt accidents as modeled in risk studies result in severe consequences to the environment of a nuclear power plant, only if the containment function of the plant is assumed to fail during the accident. To protect the containment function of a pressurized water reactor with double containment during a coremelt accident against the dominant late failure modes, a relief condenser vent system, if useful or necessary, in combination with an outside spray cooling between the primary steel containment and the secondary concrete containment, is proposed. The outside spray cooling system supports the removal of the decay heat by condensing evaporated sump water at the primary containment shell. Pressure buildup caused by the generated noncondensable gases is effectively limited by the relief condenser vent system located within the primary containment. Thereby, a relatively small flow of the steam-gas mixture in the containment is first guided through a condenser where most of the steam is condensed. The remaining noncondensable gases are then released via a conventional outside filter train in a controlled manner. Safety problems due to hydrogen combustion, which may arise due to the operation of the proposed system, can be prevented by design and operation of the system. By venting, the containment atmosphere is finally inerted.