WILMINGTON, Del/NEW YORK (Reuters) - The owners of the unfinished Vogtle power plant in Georgia led by Southern Co (>> Southern Co) agreed to cap Toshiba Corp's (>> Toshiba Corp) responsibility for its guarantees on the much-delayed nuclear project, helping ease the Japanese electronics maker's financial stress, people familiar with the matter said on Sunday.

The agreement pegs Toshiba's guarantees for the unfinished Vogtle plant at about $3.6 billion, payable over at least three years, the people said, adding the deal was not yet final.

The deal is also contingent on the owners of the incomplete V.C. Summer power plant in South Carolina, including utility company SCANA Corp (>> SCANA Corporation), coming to a similar agreement with Toshiba, said the people, who could not be identified because the talks are not public.

Toshiba's Westinghouse subsidiary is building the nuclear power plants for the U.S. utility companies, but filed bankruptcy in March because of cost overruns.

Toshiba's public shares have fallen by more than 40 percent, since it disclosed it would likely have to record billions in writedowns related to its U.S. nuclear business late last year. It said last month there was "substantial doubt" about its ability to continue as a going concern.

Toshiba had said bankruptcy for Westinghouse would allow it to limit further exposure to costs at the projects. Reaching agreements with the owners is an important step toward resolving the company's financial problems. The company is also selling its chip business, estimated to be worth at least $17.7 billion to plug a $9 billion hole in its accounts.

Toshiba and Westinghouse declined to comment. SCANA did not immediately return a request for comment.

"We remain in discussions with Toshiba to add structure to their payment obligation under the $3.68 billion parent guarantee," said Jacob Hawkins, a spokesman for Southern Co's Georgia Power unit. "We will take all actions necessary to hold Westinghouse and Toshiba accountable for their financial obligations, including the parent guarantee."

Southern Co said on Friday it would take over management of the Vogtle project from Westinghouse, after Westinghouse rejects its construction contract in bankruptcy.

It is more cost-effective for both the Vogtle and V.C. Summer nuclear power plants to be completed together, the people said. Southern is assessing the cost to complete the project.

The plants are the first nuclear projects to be built in the United States. in more than 30 years.

Toshiba had first tallied nearly $7 billion in contingent liabilities and guarantees stemming from the nuclear projects.

(Reporting by Tom Hals in Wilmington, Del. and Jessica DiNapoli in New York; Editing by Nick Zieminski and Peter Cooney)

By Tom Hals and Jessica DiNapoli

Stocks treated in this article : SCANA Corporation, Southern Co, Toshiba Corp