Homeowners in more than half of Fire Island’s communities have now accepted Suffolk’s appraisals and signed contracts, allowing dunes to be built on their land, county officials said.

In June, work on the federal flood-control project could begin in nine hamlets stretching from Fair Harbor to Seaview, said Gilbert Anderson, Suffolk’s public works commissioner.

The lead agency, the U.S. Army Corps of Engineers, and the state Department of Environmental Conservation should soon approve the homeowners’ contracts, he said.

Storms, overbooked dredgers and complicated real estate issues have delayed the $207 million project for almost two years.

Work is largely finished in Smith Point County Park and in Kismet, Seabay Beach and Saltaire, and underway by the lighthouse and in Robert Moses State Park.

Suffolk, which must obtain the land needed for the project, might not sign contracts for the barrier island’s remaining six communities, all on the east end, until September, Anderson said.

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Almost all of the nearly two dozen oceanfront homes slated for buyouts to clear the path for the new dune are located in Ocean Bay Park, in the east, where homeowners are weighing offers.

Also in the east, 13 beachfront homes in Davis Park have to be moved or realigned; about a dozen pools and decks in the Pines must be relocated.

Suffolk recently presented its proposals to homeowners in Davis Park and the Pines.

Reactions were mixed. Bill Russell of St. James said he was “extremely pleased” with Suffolk’s professionalism and cooperative proposals for moving his two-story, five-bedroom Davis Park home back about 14 feet.

“Though some changes might have to be made to the entryway, such as relocating a ramp, we’re looking forward to being in our home for years to come,” he said.

But Robert Spencer of Manhattan, who has had an oceanfront home in Davis Park since the late 1950s, said he first was told it would be moved back 20 feet, but now faces a 30-foot move that puts him right next to his second-row neighbor.

Suffolk has promised to obtain all the permits and variances homeowners will need from Brookhaven Town.