American was first out of the gate with a systemwide, available to all members Double Elite Qualifying Status miles promotion. Not too long after United matched the offer.
Both offers run until Jun 15, 2009 and both are only valid on mainline or express (American Airlines, American Eagle, or AmericanConnection, United and United Express) flights. Code-share flights operated by partner airline do not count towards the double qualifying miles.
You have to register for the offers to be eligible, more details and registration via the links below
For the American offer, see here
For the United offer, see here