The court ruled earlier this year that the state Natural Resources Department was required to compensate 87 landowners near Grand Lake St. Marys in western Ohio.
Lawyers for the landowners allege the state has been dragging its feet ever since, and the Supreme Court on Friday set a December hearing for the state to respond.
The state argues the charges of a delay are without merit.
At issue is a horseshoe-shaped dam the state built in 1997 that landowners say has led to significant floods almost every year since.
Grand Lake St. Marys is between Dayton and Toledo.