In a game of Dead Running, the GM has several duties to keep the story flowing.
Interesting Opposition - The GM should always use interesting obstacles and opponents. A retinal scanner is more interesting than another locked door and a blackmailed father is more interesting than another thug. Also, it's the duty of GM to create interesting alternatives for tests. When a player tests to steal a car, "you fail" is much less interesting than "the car's owner sees you and comes running, with a knife."
Encourage Suspicion - When the players narrate, the GM should offer ideas to make characters more suspicious. When the GM narrates, all manner of NPCs, opponents, and even obstacles can be used to breed suspicion among the characters. Maybe the police only hassle half the team, maybe thugs kidnap a character and suddenly return him without injury, maybe an opponent keeps giving signals to one of the characters, etc. Little things like these can go a long way to set the mood of the game.
Spend Harm - The player lost a test. The GM was about to narrate an awesome defeat, but the player took a re-roll. Now it's the GM's duty to use the harm generated to make things tougher for the rest of the group! Spend that harm. Spend it!
Bring it Together - The toughest duty the GM will face is tying the whole tangle of plot together. If one player narrates rabid dogs tracking the courier team and another narrates secret microchips, it falls to the GM to tie these threads together with implanted tracking dogs or the like. Some threads can't be tied together, and that's fine, but it's the duty of the GM to create the most entertaining and sensible story possible.
Settle Disputes - This is when the GM steps in to mediate. When one player claims he stole narration before she did, the GM is the final word. If two players both want to start the next scene, the GM chooses one. Should pirates begin fighting ninjas during the game, the GM settles the debate.