Which commercial aircraft can stay in the air the longest? Which commercial aircraft, when fully loaded with fuel (and passengers and luggage up to its max takeoff weight), could stay in the air the longest without landing, and how long could it stay in the air? What conditions would it need to have maximum possible endurance if the plane had no intended destination to land or particular flight path? (This is for a fictional story.)

Note: I was thinking commercial jetliners when I wrote that, and I still am, but I was accidentally unclear about it. That's preferably what I'm looking for, though.
A commercial airship, like the 'Zeppelin NT' can stay airborne for 24 hours.

The record (for a military US-Navy blimp in the 1950s) is 264 hours, 12 min. It covered more than 13,000 km.


  Record flight of 8,216 miles in 264 hours. Lakehurst NJ to west Africa to Key West FL non-stop. (Source)