Islamic State's executions of Christians show the group is exploiting Libya's lawlessness but tribal and political loyalties and the absence of a sectarian divide mean it is unlikely to grow as rapidly there as in Iraq or Syria.
On Sunday, the militant group published a video purportedly showing the execution of 30 Ethiopian Christians in two locations in eastern and southern Libya, two months after it beheaded 21 Egyptian Copts there.
The video suggests Islamic State, which controls much of Syria and Iraq, has managed to further expand in the North African country after establishing a limited presence in the eastern town of Derna as well as in western and central Libya.
It is benefiting from chaos in oil-producing Libya, where two governments allied to armed factions are fighting each other on several fronts four years after the fall of Muammar Gaddafi. With neither side able to dominate, a security vacuum exists.
But Islamic State may struggle to expand as it has in Syria and Iraq because Libya has no Sunni-Shi'ite divide the group could exploit to draw in supporters. Libyans are Sunni Muslims.
The militant group also lacks strong ties to large Libyan tribes, and must compete with former anti-Gaddafi rebel groups that have carved out their own fiefdoms based on regional, tribal, ethnic and political ties.
"These groups are ultimately self-serving and self-interested," said Geoffrey Howard, Middle East and North Africa analyst at Control Risks.
"IS's advances are likely to pose a threat to their own political and economic agendas, as well as their control over territory and strategic assets."
That has left Islamic State splintered into small units that can launch high-profile attacks but whose grip on territory is not firm enough to build up social services, as the group has done to win over local people in places like Iraq's Mosul.
Unlike in Iraq and Syria, Islamic State insurgents have not occupied any oilfields in Libya to generate revenues, and selling oil outside official channels would anyway be more complicated in Libya than in the two other Arab countries.
With oil storage facilities located in coastal areas, Libyan oil is exported by sea. Some Libyan warring factions have tried to sell oil independently from ports under their control but a U.N. embargo has deterred foreign shippers.
Cross-border oil smuggling would also be difficult as Islamic State controls no Libyan land border.
Videos showing executions and portraying Christians as "crusaders" could help Islamic State attract more fighters from abroad or from local militant groups such as Ansar al-Sharia.
"They want to send a signal to Libyan jihadists that they are the really tough guys," Mattia Toaldo, policy fellow at the European Council on Foreign Relations, told the Reuters Global Oil Forum. "The attraction of Tunisian and Sudanese jihadists gives Islamic State a big potential."
But the biggest security headache for Western powers would be an Islamic State expansion into Libya's southern Sahara, the apparent location for part of Sunday's video.
Neither Libyan government holds much sway in the remote area bordering Niger, Chad, Sudan and Algeria, which has been long neglected. Gaddafi made local tribesmen promises of citizenship and development projects but never delivered.
Southern tribes make a living by smuggling anything from subsidized petrol, flour and weapons to African emigrants heading for Europe across Libya's porous sub-Saharan borders.
In January, Islamic State posted a recruitment video in a Tuareg language, calling on aggrieved tribesmen to join with their promised caliphate.
Analysts say recruiting in the south would help Islamic State co-operate with other militant groups, such as Tuaregs fighting in Mali or Nigeria's Boko Haram as it tries to take its battle to Libya's neighbours Chad and Niger.
The militants also benefit from the reluctance of Libya's warring governments to tackle them, analysts say, as each wants Islamic State to keep the other busy.
War planes belonging to the internationally recognised premier Abdullah al-Thinni have made air strikes near the central city of Sirte on forces loyal to the rival government, which controls Tripoli. But they have spared militants inside Sirte, where Islamic State has taken over government buildings.
Forces loyal to Tripoli have meanwhile moved heavy guns to the outskirts of Sirte but not launched a full assault on the Islamists fighting Thinni's forces in the east, although there have been smaller clashes outside the city.
While Thinni misses no opportunity to warn about Islamic State's expansion, Tripoli officials tend to downplay the group as Gaddafi loyalists with little power.
"The terrorist groups cannot terrorize the main cities. They only sneak into small towns," said Amina Mahjoub, an Islamist member of the Tripoli-based rival parliament.