At the headquarters of the Syrian Democratic Forces in Ainissa, the normally bustling offices were thinly populated on a recent day as the Kurdish-dominated coalition shifted its fighters to battle against the Turkish invasion in northwestern Syria.
Haqi Kobani, the deputy commander of the S.D.F., was holding down the fort in his capacious office, where a portrait of Abdullah Ocalan, the imprisoned leader of the Kurdistan Workers’ Party, or P.K.K., had pride of place. While Kurds hold most of the leadership positions, the S.D.F. is a majority Arab force now, engaged with the Americans in the fight against the Islamic State, mostly in Arab rather than Kurdish areas of Syria.
“Arabs love Abdullah Ocalan too,” Mr. Kobani said, casting a glance at the portrait. “There’s nothing hidden from our side. Everything we do is obvious and clear to the world.”
Many Arabs would probably differ about their love of Mr. Ocalan, whose socialist, radically egalitarian philosophy of governance holds sway throughout the autonomous region, known as Rojava, that the Kurds have carved out in Syria, with the help of the American-led international coalition. Their uneasy alliance, held together by the fight against the Islamic State, could be severely tested as the Kurds expand their control.
Kurdish aspirations will also come up against an implacable Turkey, which regards a self-governing Kurdish region across its southern border, and controlled by the P.K.K., as nothing short of an existential threat. Those fears led to the offensive against Afrin, the eastern region of Rojava, and Turkey has even talked about attacking further east, which would put it in conflict with American forces.
In the face of those daunting obstacles, the Kurds have been slowly and systematically building Rojava, knowing that eventually the war would end and the truly difficult job of managing the peace would begin.
For six years they have been establishing local and regional governments, sending foreign affairs representatives abroad, collecting taxes, organizing socialist communes and raising militias. They often describe their revolution as “the project” or “the experiment,” the implementation of local self-governing democracy, freedom and equality for women and a socialist system inspired by anarchist and Marxist philosophies.
As the Islamic State has crumbled in the eastern part of Syria controlled by the Americans and the Syrian Democratic Forces, the Kurds have moved into what had been majority Arab areas, bringing Mr. Ocalan’s principles and governing philosophy along with them. Self-administration governments, after the Kurdish model, have been established in the city of Manbij since the Islamic State was defeated there in 2016, and recently even in Raqqa, after the coalition and their Kurdish-led allies drove the extremists from their self-declared capital last year.
On a recent visit to the predominantly Arab city of Manbij, outside Rojava, strains between the Kurdish leadership and the Arab populace were clearly visible, despite official efforts to deny the problem. But there were also signs of acceptance.
An Arab schoolteacher said most Arabs in the town were unhappy with what they see as a Kurdish government, but were afraid to speak out. For visiting journalists, it was difficult to speak to Arab residents without government minders insisting on being present.
Many Arabs, the schoolteacher said, speaking on the condition of anonymity because he feared detention, have been particularly unhappy since the reported arrests in early January of two Arab men, whose bodies were found 17 days later, dumped on the highway outside town.
Government officials at first promised journalists that they could visit family members of those who were killed, and also meet with a committee of Arab elders, set up to investigate the killings. The officials said both groups had absolved the Kurdish authorities of blame.
But the visit to the families was denied, and while the meeting with the committee did take place, it happened only in front of half a dozen Kurdish officials. Reached independently later, at the village of Kabor Emo outside Manbij, the father of one of the victims had a different story.
“It was the democratic government, I blame the democratic government,” said the father, Muhammad Omar al-Masri, but then he broke off the interview as villagers became angry and agitated at visitors.
Dealing with Arab populations is not the only problem that Mr. Ocalan presents for Kurdish aspirations. The group he leads from prison, the P.K.K., is a designated terrorist organization to Western countries, including the Kurds’ American allies. The Syrian Kurds claim they have nothing to do with the P.K.K., but Mr. Ocalan’s cultlike popularity in Rojava argues otherwise.