Two Chesapeake Energy Corp. (NYSE: CHK) directors -- members of the audit committee now dealing with the personal finances of the company's CEO -- offered their resignations Friday after they attracted little support at the annual shareholders meeting.

Under Chesapeake's old bylaws, Richard K. Davidson and V. Burns Hargis would have won re-election to the company's board of directors, with about 27 and 26 percent of the shareholder votes cast, respectively. However, the Chesapeake board adopted a new majority-vote bylaw proposal, so both tendered their resignations, the company said in a statement.

Each is a member of the board committee charged with investigating Chesapeake CEO Aubrey McClendon's use of loans and company overspending that wiped out $2.6 billion in market value, Bloomberg News reported.

Chesapeake said it will review the resignations in due course.

The company is the second-largest producer of natural gas in the U.S., and it has historically been very aggressive in accumulating leasing rights in the nation's unconventional gas plays. But its financial statements have been pressured as development of the country's shale resources has dramatically risen and the price of natural gas has dramatically fallen.

As a result, Chesapeake is being forced to part with a number of assets, with the company planning to sell $12 billion worth of them this year. Last month, the company secured a $4 billion loan from the Goldman Sachs Group Inc. and Jefferies Group Inc.

In Friday's trading, Chesapeake gained 51 cents, or 2.86 percent, to close at $18.36 a share.