Following their statement last month that they would return some artefacts to Italy, the Getty has now also announced the details of two artefacts which will be returned to Greece.
It is interesting to note that these various negotiations with Greece & Italy (& presumably other parties as well?) are continuing despite (or perhaps because of) the ongoing trial of former curator Marion True in Italy.
There are a number of interesting points to note from this announcement:

1. The Getty was eager to resolve the issue rapidly to improve their working relations with Greece: Mr. Brand said the museum decided to give up title to the stele and votive relief even though negotiations are incomplete because the Getty was eager to establish a new working relationship with Greece.
   
2. Greece hopes that this agreement will help to pave the way for the return of other antiquities illegally residing in foreign museums: At a news conference in Athens, Mr. Voulgarakis said the breakthrough would lent momentum to Greece’s bid to recover additional antiquities from museums in the United States and Europe.
3. One of the keys to securing the return of these two artefacts was a change of director at the Getty – the implication of this is that the new head of the institution, Michael Brand, sees the benefit of negotiating such claims rather than ignoring them: For the first time in 10 years, we had a Getty director coming to us with a proposal to work things out,” said Ms. Vassilopoulou, who took part in the negotiations.

From:
New York Times

Getty Museum Will Return 2 Antiquities to Greece
By HUGH EAKIN
Published: July 10, 2006

After months of intense scrutiny of its collection of Greek and Roman antiquities, the J. Paul Getty Museum in Los Angeles said today ay that it had agreed to relinquish ownership of two of four rare ancient works that the government of Greece says were illegally removed from within its borders.

The compromise accord, which was initially reached in May at a meeting in Athens between the museum’s director, Michael Brand, and the Greek culture minister, Georgios A. Voulgarakis, provides for the return to Greece of a large stele, or grave marker, acquired by the museum in 1993 and a small marble relief from the island of Thasos bought by the museum’s founder, the oil magnate J. Paul Getty, in 1955.

The Getty has not yet worked out the formal arrangement under which the stele and the relief will be repatriated, but officials said the accord might include a provision for long-term loans from Greece. Talks are continuing on the other two objects sought by the Greek government, with goal of reaching an accord by late August, officials said.

Mr. Brand said the museum decided to give up title to the stele and votive relief even though negotiations are incomplete because the Getty was eager to establish a new working relationship with Greece.

“These talks have been going on a long time, and it seemed like a good idea on both sides to start making some progress,” Mr. Brand said today in a telephone interview from Australia, where he was traveling.

At a news conference in Athens, Mr. Voulgarakis said the breakthrough would lent momentum to Greece’s bid to recover additional antiquities from museums in the United States and Europe.

“This is a very important day,” he said, adding, “We’re confident that ongoing talks will yield the results we want.”

Although the grounds for the Greek claim to both objects being returned by the Getty are clear, both sides said, the circumstances of their removal from Greece are very different.

The 2,400-year-old stele was bought by the Getty in 1993 from Safani Gallery, an ancient art dealer in Manhattan, and it had not been documented in published reports. Bearing an arresting image of a dead warrior named Athanias, it is a rare example of incised black limestone from Boeotia, in the area of Thebes in ancient Greece.

Although there is no hard evidence of an unlawful excavation, Mr. Brand said, the museum determined in a scholarly review that such a work — unlike, say, Greek vases — were not made for export in ancient times and could only have been removed from Boeotia.

The marble relief — which dates from 500 to 480 B.C. and shows two female figures approaching the shrine of a goddess, possibly Aphrodite — has been identified as part of a group of pieces excavated by French archaeologists on Thasos in 1911. Greek officials say it was stolen from a storeroom at the French Archaeological School in Thasos soon afterward and eventually entered a private Austrian collection before it was bought in 1955 by Mr. Getty in London.

“This is a piece where we know where it belongs, at a site, and it will be reunited with that group,” Mr. Brand said.

The other two valuable works claimed by Greece, a fourth-century B.C. gold funerary wreath adorned with blue and green glass inlay, and a sixth-century B.C. marble kore, or statue of a young woman, were acquired in 1993 and are prominently displayed at the Getty Villa, the home of the museum’s antiquities collection in Pacific Palisades, Calif.

The kore has also been claimed by the Italian government. According to a Getty Museum publication, the statue is made from marble from the Greek island of Paros and was acquired through the “European art market.”

Although Greece first laid claim to the four disputed objects in the 1990’s, negotiations did not begin in earnest until last fall, when the Greek Culture Ministry submitted a new request for the four pieces. Late last year, a few weeks before he officially took the reins of the Getty Museum in early January, Mr. Brand contacted the Greek Culture Ministry to open negotiations on the objects. In May, he traveled to Greece to broker a settlement.

After that meeting, he said in a statement that he would recommend that the Getty’s board of trustees approve the return of “some of the claimed antiquities in the near future.” The board unanimously approved the return of the stele and the marble relief in mid-June.

Vivi Vassilopoulou, director of antiquities at the Greek Culture Ministry, said Mr. Brand’s “placating” style had been pivotal to the deal.

“For the first time in 10 years, we had a Getty director coming to us with a proposal to work things out,” said Ms. Vassilopoulou, who took part in the negotiations.

The agreement comes as the Getty is trying to resolve a much larger claim by Italy for 52 objects in its collection, while coping with Italy’s indictment of its former antiquities curator, Marion True, on charges of conspiring to acquire looted artifacts.

The Italian claim against the Getty includes numerous objects acquired by Ms. True and other curators for the museum that have been traced by Italian prosecutors to Giacomo Medici, an Italian dealer who was convicted in 2004 of trafficking in illicit antiquities.

The Italian evidence record says that the kore sought by Italy and Greece was acquired by the Getty from a London dealer, Robin Symes, in June 1993. The object appears in several photographs seized from a Medici archive in Switzerland, “evidently dirty with soil, and with breaks that are very fresh,” the evidence record says. The Italian record says that the kore was never exhibited or published before the Getty bought it.

After talks in Rome in late June, the Getty announced that it had reached a tentative agreement with the Italian government to return some of the objects in dispute, including “several masterpieces,” although it gave no specifics. Mr. Brand will report formally to the Getty’s board on those June discussions when he returns to Los Angeles later this month.

Mr. Brand said it was likely “that there would be a couple of objects — or some objects — that will require further discussions.” But he added that in the next two or three months, “a significant part” of Italy’s claim “could be resolved.”

It remains unclear how such an accord might affect the trial of Ms. True, which began in November.

In the months preceding Mr. Brand’s negotiations in Athens, Greek officials opened their own investigation of Ms. True, who has a vacation house on the Greek island of Paros, and of Christos Michaelides, a Greek dealer of antiquities with close ties to the Getty, who died in 1999.

In two raids this spring, Greek officials entered Ms. True’s house and confiscated a small number of antiquities. Greek prosecutors have also threatened to press charges against Ms. True for possessing antiquities that had not been registered with the authorities.

Yet lawyers for Ms. True say that the confiscated artifacts were already in the house when she bought it in 1995.

Asked what antiquities claims Greece would pursue next, Mr. Voulgarakis declined to give specifics. Nor would Ms. Vassilopoulou, but she said, “We’re aggressively compiling evidence that establishes Greek provenance and ownership for all of these disputed items.”

Anthee Carassava contributed reporting from Athens for this article.