One of the bidders of Irvine-based Billabong USA's Australian parent has withdrawn its offer, the action sports apparel maker and retailer said Wednesday.

Billabong International Ltd. earlier this month said it had received a second bid to buy the company for $708 million, matching a July offer for the company made by Texas-based private equity firm TPG Capital LP.

The identity of the second party was kept confidential, but reports speculated it came from Bain Capital LLC, the Boston-based private equity firm cofounded by Republican presidential nominee Mitt Romney.

TPG is conducting due diligence, while Billabong said it is continuing to evaluate its sale options.

Billabong makes clothes, shoes and accessories under a number of brands. Those include RVCA, DaKine and Element.

The news comes just a few days after competitor Rip Curl Pty. Ltd., also of Australia, said this week it hired Merrill Lynch to advise on the surfwear and apparel company’s possible sale. Rip Curl, which has local offices in Costa Mesa, said it had been approached by several companies.

The Australian Financial Review newspaper reported Rip Curl could sell for as much as $525 million. That would be roughly 10 times the company’s project 2013 earnings before interest, taxes, depreciation and amortization of $49 million.