US officials have begun investigating whether ties between the boards of Google and Apple violate anti-trust laws, according to reports.

Apple and Google share two directors - Google CEO Eric Schmidt and Genentech chairman Arthur Levinson - and the US Federal Trade Commission (FTC) is examining whether it affects competition between them.

Federal law prohibits a person's presence on the boards of two companies that are direct rivals.

Google and Apple are competitors in the mobile phone market, with Apple's iPhone coming into increased rivalry with phones using the Google-produced Android operating system.

Legal experts say the issue is rarely pursued partly because it is difficult to prove how overlapping directors impinge on business decisions. Mr Schmidt has said he recuses himself from Apple board meetings when the iPhone is discussed.

The Clayton Anti-trust Act of 1941 prohibits a person being a member of the boards of two rival firms at once if it reduces competition between them. "Government actions under Section 8 are rare, but they are brought under circumstances when the presence of a common director on competing boards is likely to be anti-competitive, " Andrew I. Gavil from the Howard University School of Law told the New York Times.

Mr Schmidt was asked to join the Apple board by CEO Steve Jobs in 2006. Since then the areas in which the two companies overlap have grown. They have competing web browsers Safari and Chrome, competing music and video websites iTunes and YouTube as well as a host of competing computer software applications including email, photo-sharing and cloud computing.

Dr Levinson has served on the board at Google since 2004 and at Apple since 2000. He has been a senior executive at Genentech, one of the world's leading biotech companies, since 1989.

This is the second anti-trust inquiry to involve Google in recent days.

Last week the Department of Justice started an investigation into the company's $125m settlement with authors and publishers to digitise millions of books.

The new investigation "appears to be in early stages," the New York Times said, and the agency has alerted the companies. Both companies declined to comment. In most instances the solution is for the executive in question to step down from one of the two boards.

The inquiry comes after Mr Schmidt was appointed as a senior advisor to President Barack Obama on technology, becoming a member of the Council of Advisors on Science and Technology, a 20-strong group that will help formulate policy in a number of areas "where understanding of science, technology and innovations is key to strengthening the economy".

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