New Delhi, May 31 -- Two of America's most powerful oil companies delivered back-to-back warnings last week that the world is running out of the crude stockpiles that have so far prevented the Iran war from triggering an energy crisis of the most acute kind. Executives at both Exxon Mobil and Chevron told a Wall Street conference that inventories are approaching a threshold beyond which oil prices have only one direction to travel.

The more alarming of the two assessments came from Exxon Mobil senior vice president Neil Chapman, who told the conference hosted by investment bank Bernstein in New York that the pace at which global crude stocks are falling has no modern precedent.

"We're approaching unheard of inventory levels," Chapman sa...