The U.S. has sent a team of American soldiers to Libya to work out details of a training program being set up in Bulgaria for the new Libyan Army. In late 2013 the U.S. agreed to establish a training facility in Bulgaria where 500 American soldiers would serve as instructors at a camp that would train 8,000 (or more) Libyan recruits in basic military skills.
Putting the training facility in Bulgaria avoided the possibility of the many Islamic terrorist groups active in Libya having American instructors as targets for kidnapping for murder. Many Islamic terrorist organizations in Libya see the Libyan Army as the enemy and a training facility with American staff would be a prime target. The small team of officers and NCOs will work with their Libyan counterparts to agree on what exactly the training will cover and how selection for the training will be conducted. This small team of American troops will receive a lot of protection while in Libya.
The first batch of 200 Libyan trainees is to go to Bulgaria soon. Some 500 soldiers from the U.S. 1st Infantry Division have been selected as instructors. Bulgaria will provide military and civilian personnel for support services and some Libyan Army officers and NCOs will be in Bulgaria to oversee the entire process.
While American Special Forces often train foreign troops, for jobs like this, that mainly provide basic skills, its easier, cheaper and more convenient to use regular troops (who do this sort of thing with Americans all the time.)