US President Barack Obama announced on October 21 that US troops would depart Iraq by year`s end, after negotiations with Baghdad on a larger-scale post-2011 US military training mission broke down.
The military personnel and contractors are part of the Office of Security Cooperation - Iraq (OSC-I), which falls under US embassy authority, Lieutenant Colonel Tom Hanson, director of strategic communications for OSC-I, told AFP.
"The 157 (military personnel) are here, and the up to 763 number is based on the number of active foreign military sales cases at any given time," he said.
As not all are active at once, the 763 contractors will probably not be in Iraq at the same time, he added.
The contractors are "involved in some aspect of bringing the equipment to the Iraqis and helping them learn how to operate it, and bringing (them) to a minimum level of proficiency on it, whether it`s a tank or an airplane or an air traffic control system or a radar," Hanson said.
Meanwhile, "most of the uniformed personnel are programme managers, so they`re supervising contractors."
The aim "is to help the Iraqi security forces build their capability, build the proficiency, and modernise their equipment," he said.
The contractors are not required to be American citizens, Hanson said, adding that there are OSC-I contractors of various nationalities, including some Iraqis.
OSC-I military personnel have immunity from Iraqi prosecution, but the contractors do not.
"The uniformed military personnel are protected the same way that the diplomats in the embassy are. The contractors do not have any immunity, any legal protections right now," Hanson said.
The issue of immunity scuppered the talks on a post-2011 US military training mission. Washington insisted that the trainers must have immunity, while Baghdad said that was not necessary.