Facts from a 2008 Report to Congress: (This info is still current on activations):

Three stages of incremental activation allow for tailoring an airlift force suitable
for the contingency at hand.11 The stages of activation are as follows:
Stage I — minor regional crises.
Stage II — major theater war.
Stage III — periods of national mobilization.

The commander, U.S. Transportation Command (TRANSCOM), with approval
of the Secretary of Defense, is the activation authority for all three stages of CRAF.

During a crisis, if the Air Force Air Mobility Command (AMC) has a need for
additional aircraft, it would request the TRANSCOM commander to take steps to
activate the appropriate CRAF stage. Each stage of the CRAF activation is only used
to the extent necessary to provide the amount of civil augmentation airlift needed by
DOD. When notified of call-up, the carrier response time to have its aircraft ready for
a CRAF mission is 24 to 48 hours after the mission is assigned by AMC.
The air
carriers continue to operate and maintain the aircraft with their resources; however,
AMC controls the aircraft missions.

CRAF has been formally activated on two separate occasions over the
program’s 57-year history.

The first instance occurred for Operations Desert
Shield/Storm from August 18, 1990, through May 24, 1991, and included long-range
international passenger and cargo segments up to Stage II. During Operation Desert
Storm, CRAF airlines executed 5,460 missions transporting 726,000 passengers and
230,000 tons of cargo at a cost of $1.4 billion.

The second activation, during
Operation Iraqi Freedom, lasted from February 8, 2003 through June 18, 2003, and
included the long-range international passenger segment up to Stage 1 — long-range
cargo requirements were met organically or with voluntary commercial contracts.
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Typically, buried in the employment requirements one signs on new hire day, is that you accept being a CRAF pilot volunteer for your airline. If you happen to be on the fleet that is enrolled in CRAF at your company, your subject flying CRAF. Check your contract