A variety of Bain funds in the Romneys’ portfolio have controlling stakes in foreign companies. Had those funds been set up in the United States, the Romneys and other American investors would probably have been subject to certain federal taxes for their ownership of “controlled foreign corporations.” Setting up the funds in the Caymans allowed them to avoid those taxes.

“Bermuda and the Caymans are popular choices for U.S.-based funds because they’re both close by and neither imposes local taxes on the fund or its owners,” said Andrew W. Needham, a partner in the tax department at Cravath, Swaine & Moore L.L.P.

Another appeal of offshore funds is that they help private equity attract investment from deep-pocketed big institutions like pension funds and university endowments. While these are generally tax-exempt, they are liable for taxes on “unrelated business taxable income” if they put money in funds that use debt financing to make investments.

Bain and other private equity firms use a variety of mechanisms to help investors avoid those taxes, including setting up offshore “blocker” corporations, a practice that has been criticized in some circles and has prompted legislative efforts to curb it. These offshore corporations become a conduit for money for these institutional investors, as well as foreign investors looking to avoid United States taxes.

Individual retirement accounts, as tax-exempt entities, are subject to the “unrelated business income” tax. But people familiar with Mr. Romney’s investments said his I.R.A., which is managed by an independent trustee and is estimated to be worth between $21 million and $102 million, used offshore blockers to avoid the tax. Mr. Romney’s I.R.A., for instance, has millions invested in several Sankaty funds with onshore and offshore investment vehicles. His I.R.A. would have invested through the offshore funds, they said.

In addition, the largest investment — worth up to $25 million — in Mr. Romney’s I.R.A. is in a fund called BCIP Trust Associates III, a Cayman Islands partnership through which Bain employees invested in the firm’s deals. Documents from a German regulatory authority, detailing the Bain funds’ share of a media holding company in that country, refer to holdings by BCIP Trust’s blockers, indicating it used such entities.