The battle Wednesday reflected a growing problem for the U.S. and its push to train local fighters, even as those forces take territory from ISIS. Who exactly will govern those towns now? Will it be the Kurds who have led the fight against ISIS? Or will it be what some in the Pentagon have privately called the “token Arabs” trained by the U.S. to accompany them?

Two defense officials told The Daily Beast Wednesday they don’t know. They believe the Arabs would be in charge. But even these officials admit that asking the 5,000-or-so newly-trained Arab fighters to control three or more formerly ISIS-controlled areas—and at the same time move into the ISIS capital of Raqqa—would be difficult.

On the other hand, some worry that a Kurdish controlled Manbij could be ethnically cleansed, creating the kind of Sunni disenfranchisement that led to the rise of ISIS. The fall of Manbij into Kurdish hands, however, would give the Kurds a contiguous region in northern Syria. Moreover, a Kurdish controlled Manbij could draw the ire of U.S.-allied Turkey, which rejects a Kurdish controlled region on its border.

The question “what happens after ISIS?” looms increasingly over the U.S.-led effort.