The think tanks do not disclose the terms of the agreements they have reached with foreign governments. And they have not registered with the United States government as representatives of the donor countries, an omission that appears, in some cases, to be a violation of federal law, according to several legal specialists who examined the agreements at the request of The Times.

As a result, policy makers who rely on think tanks are often unaware of the role of foreign governments in funding the research.

Joseph Sandler, a lawyer and expert on the statute that governs Americans lobbying for foreign governments, said the arrangements between the countries and think tanks “opened a whole new window into an aspect of the influence-buying in Washington that has not previously been exposed.”

“It is particularly egregious because with a law firm or lobbying firm, you expect them to be an advocate,” Mr. Sandler added. “Think tanks have this patina of academic neutrality and objectivity, and that is being compromised.”