The multimillionaire philanthropist had fled the United States in April for Cuba and was arrested Tuesday night in Berlin after taking a flight from Zurich. Axelrod, 76, is charged with defrauding the Internal Revenue Service in a business matter, but that inquiry opened up questions about whether he had deliberately exaggerated the value of instruments he gave the Smithsonian and the New Jersey Symphony Orchestra to get a substantial tax break. Orchestra officials say the FBI is reviewing that transaction.

Beginning in 1986, Axelrod, a New Jersey businessman who made millions in pet products and pet care books, lent the National Museum of American History four Stradivarius stringed instruments: a 1687 violin, a 1709 violin, a 1695 viola and a 1688 cello. The instruments, which collectively were known as the Axelrod Quartet, were formally given to the museum in December 1997. At the time the collection was said to be valued at about $55 million, making the donation one of the largest in the Smithsonian's history.

Questions about the value of the gifts, and the tax breaks for the gifts, are not part of the federal case, said Michael Drewniak, a spokesman for the U.S. attorney in Newark, N.J. "The charge has not changed," said Drewniak.

Sen. Charles E. Grassley (R-Iowa), chairman of the Senate Finance Committee, asked the Smithsonian for a history of its association with Axelrod and has called a hearing for next Tuesday to look into "overvalued deductions."

Smithsonian officials say it is not their policy or the procedure of any museum to do independent appraisals of gifts.

"The Smithsonian does not provide donors with appraisals or fair market valuations of items donated to its collection," Smithsonian Secretary Lawrence M. Small said in a letter to Grassley. "The collections of the Smithsonian are selected for their scientific, artistic, and historical significance, not their monetary value."

In documents about the Axelrod gift sent to Grassley, museum officials attached several different values to the gift. In 1986, the instruments were given an insurance value of $5 million by Smithsonian officials. The next year a value of $20 million was assigned to the quartet. Not two months later, it was listed as $30 million.

When Axelrod formally donated the instruments in December 1997, a memo from the Smithsonian general counsel's office noted a different value. "[Axelrod's] attorneys yesterday informed me that the actual valuation for tax purposes is $55 million," according to the memo.

Grassley said the papers did not clarify the Smithsonian's role in the assessment of the instruments. "The letter raises more questions than it answers," he said. "Specific to the Axelrod donation, I want to understand why the Smithsonian refers to values of these instruments that are all over the map."

Speaking of those numbers, Small said in his letter, "These values are for insurance purposes only and are not based on the object's 'fair market value,' the amount at issue when the donation is the subject of an income tax donation."

The internal memos given to the Senate, said spokeswoman Linda St. Thomas, "are not official Smithsonian statements on the value of these objects. The only time we put an official number is when we put it on an insurance policy."

When an artifact is displayed outside Washington, it is insured and the museum follows the owner's estimate. "The Smithsonian also has no involvement in the process of valuing an item so that its donor may take a tax deduction," said Small in his letter.

Axelrod has supported the Smithsonian for many years, giving $2.8 million in cash to the American History Museum, as well as the National Museum of Natural History, and donating 17 instruments. Part of his cash donation supported performances using the rare musical items.

Michael Himmel, Axelrod's defense attorney, said yesterday he had not spoken to his client since his arrest and it could take months for the U.S. attorney's extradition request to be resolved. Himmel said questions about the donations are misguided.

"During the period of time when the government was investigating his conduct [in the tax matters], they also subpoenaed documents related to his violin collection. Had the government believed back then that they had a case that they could prove concerning the value of the violins," it would have been included in the indictment. "They knew I had experts lined up who would weigh in on the true value of the instruments," Himmel said.