In February 2016 France revealed that it had at least fifteen special operations troops in Libya and they had been there since the end of 2015. The French troops were operating from an air base outside the eastern city of Benghazi and were working alongside British and American special operations forces and some other specialists from all three countries. While there were less than 200 foreign troops involved all the Islamic terrorist groups in Libya (and some of the less religious ones) see this presence of foreign troops tantamount to a Western (and non-Moslem) invasion of Libya. Most Libyans don’t care. The air base is controlled by the elected Libyan government that is recognized by the UN and on the verge of getting the majority of armed groups in the country to recognize one government and unite against the violent and unwelcome presence of ISIL (Islamic State in Iraq and the Levant).
The Western commandos are mainly training their Libyan counterparts as well as helping to establish a more efficient intelligence network so that Western warplanes can carry out more strikes on ISIL. Few Libyans object to anything that will hurt ISIL. The French said their troops had carried out four missions so far but nothing was said of how many, if any, the American and British had engaged in. Back in 2013 Islamic terrorist groups tried to conquer Benghazi but failed. Despite that there are still some Islamic terror groups which refuse to leave the city and fight to the death when pressed over the issue.
The internationally recognized government set up shop in the small port city of Tobruk (1,600 kilometers east of Tripoli) after encountering hostility from militias loyal to the pre-June 2014 elections government. Many other government offices moved as well and are finding space where they can. The rebel governments in Tripoli and the Tobruk eventually negotiated a merger deal in late 2015. Most Libyans are fed up with the continuing violence. The 2011 rebellion against Kadaffi left over 30,000 dead but the infighting since then has killed nearly as many. Most major factions agree on peace but Islamic terrorist groups in Tripoli and Benghazi, aided by tribal factions that want more power and money, continue to fight.
Many Libyans are calling for foreign intervention. So has neighbor Egypt. So far the most NATO nations will do is an occasional air strike and a small but growing special operations presence. The main justification this is the growing presence of ISIL in Libya, where the locals were unable to form a national government after the 2011 revolution.