In the event of a nuclear strike on American soil, they're going to be in a little bit of trouble. But at least we'll die safe in the knowledge that the valiant leaders of their nation—or any yahoos lucky enough to be in office at the time—will be escaping the nuclear holocaust in a fleet of environmentally-impervious airborne command centres.
The Boeing E-4 Advanced Airborne Command Post, part of a fleet of four highly-modified airliners collectively known as project Nightwatch, serve as the National Airborne Operations Center (NAOC) for the National Command Authorities. So basically, when they go to Defcon 1, whether it's due to say a terrorist attack or a North Korean nuke strike or first contact with the Borg, their leaders can take to the skies and remain out of immediate harm while maintaining full command of the country.
While the President has Air Force One, the Joint Chiefs of Staff ride on these planes, each designated as E-4B. Based on the Boing 747-200, the £157 million E-4B measures 231 feet long with a 195 foot wingspan. Its four General Electric turbofans provide 12 hours of endurance at altitudes above 30,000 feet, though with its mid-air refuelling capability, the E-4B can stay up indefinitely.
The fleet entered active service between 1974 and 1985. Each carries a crew of up to 112 crew (in addition to the VIPs) and is built to withstand virtually all attacks—nuclear, chemical, biological, direct fire, and even EMP—without a significant loss of functionality. In fact, the E-4B still uses analogue instruments in its cockpit specifically because they're less susceptible to EMP damage than more modern glass displays. The rest of the plane's systems are cutting-edge and largely classified.
This includes its communications suite. Not only does the aircraft offer satellite communications for worldwide communications, it also carries a 5 mile long spool antenna for the VLF (very low frequency) transmissions, allowing those aboard the plane to communicate directly with the nation's fleet of nuclear armed submarines up to 3,000 miles away.
The US Air Force only has four E-4B's in total with one fully fuelled on standby at all times, often within a stone's throw of Air Force One so that if the President's plane is compromised, he's got a back-up at the ready. The other three not on standby also serve a number of non end of the world functions such as ferrying FEMA crews to natural disaster sites then acting as temporary command posts until the situation on the ground stabilises. [The Aviationist - Defense Industry Daily - FAS 1, 2 - Boeing]