Paris (CNN) -- Investigators trying to determine why an Air France plane crashed mysteriously two years ago have recovered the complete contents of the flight data recorder and the last two hours of cockpit conversation, they announced Monday.

It will take several weeks to analyze the data, French air accident experts said.

All 228 people aboard Air France 447 were killed when the Airbus A330 belly-flopped into the ocean June 1, 2009, in stormy weather. The cause of the crash is still not known.

Discovering that there was data on the recorders "is excellent news. It is really going to help us work out what happened on that plane," said Martine Del Bono, spokeswoman for France's Bureau of Investigation and Analysis (BEA).

Q&A: Will the mystery of Flight 447 be solved?

The cockpit voice recorder and flight data recorder were found at the beginning of May after an unprecedented series of submarine searches of a mountain range 3,900 meters (12,700 feet) under the ocean. They were brought to the surface and taken to Paris by ship and plane.

The investigators also recovered two bodies from the fuselage -- after finding only about 50 bodies in the days immediately after the crash.

They will not bring more bodies up from the ocean if they cannot identify the two they already have, they said Thursday.

Those two bodies are being examined to see if there is enough DNA to identify them, investigators said, adding that they hope to have results by Wednesday.

If they can identify the remains, they will consider bringing up other bodies from the wreckage.

The bulk of the plane was located earlier this year and contains many more human remains, according to investigators.

Recovering more bodies will be a difficult task, with miles of cable required to bring each one up over a period of three hours, they said.

Investigators also brought an engine and an avionics bay containing computers to the surface, they said.

The pilots of Air France 447 lost contact with air traffic controllers on June 1, 2009, while flying across an area of the Atlantic known for severe turbulence, officials said. But exactly what caused the plane to plunge into the ocean remains a mystery.

The plane slammed into the water while en route from Rio de Janeiro, Brazil, to Paris, falling so fast that air masks did not have time to deploy.

The fuselage was discovered in April with bodies still inside, investigators said.

Some relatives of those who died have expressed reservations about remains being brought to the surface.

Last month Robert Soulas, head of a support group for families of flight victims, said: "For me, personally I would like to leave the bodies of my children, my two children, on the seabed."

Other relatives have called for the bodies to be recovered.

CNN's Ayesha Durgahee, Catherine Clifford and Niki Cook contributed to this report.