SAN ANTONIO, July 31 (Reuters) - A U.S. Army major and his wife were ordered held without bond on Tuesday on charges they took millions of dollars in bribes for U.S. contracts in Iraq.

John Cockerham, 41, and wife Melissa, 40, were flight risks, ruled U.S. Magistrate Pamela Mathy in a hearing.

The two have been jailed since July 22 when they were arrested at their home at Fort Sam Houston in San Antonio on charges of accepting bribes, defrauding the United States, money laundering and conspiracy while Cockerham was a contracting officer in Kuwait in 2004 and 2005.

He is accused of doing deals with favored contractors in exchange for kickbacks that his wife and a sister in Dallas, also facing charges in the case, helped pick up and launder, according to prosecutors.

In Tuesday's hearing, Assistant U.S. Attorney Mark Pletcher told Mathy the Cockerhams accepted $9.6 million in bribes and anticipated receiving a further $5.4 million from contractors and suppliers looking to get work in Iraq.

Their attorney, Jimmy Parks, said Cockerham was a decorated Army veteran and the charges against them "just don't compute."

"Right now, I think every one of us is very, very disappointed in the judge's decision," Parks said.

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