For Fidel Castro, it was victory over "Yankee imperialism"

In the Cuban papers were transcripts of the telephone communications between President Castro and his military commanders during the battle.

They showed how closely involved he was, the tension of the moment and the joy when, after more than 60 hours of fighting, it became obvious that the invasion had been defeated.

The US documents chart in detail the humiliation felt at the nature of the defeat and the embarrassment caused to President Kennedy.

CIA failure

One State Department paper puts the blame for the debacle squarely on the CIA, which trained the invasion force.

It said: "The fundamental cause of the disaster was the Agency's failure to give the project, notwithstanding its importance and its immense potentiality for damage to the United States, the top-flight handling which it required."

This has been a very emotional time, especially discussing with the colonel in charge of the operation the very intense fighting that took place in this spot

Alfredo Duran, invading force

It added: "There was failure at high levels to concentrate informed, unwavering scrutiny on the project."

In the aftermath of the failed mission, another US paper lays out the early plans to destabilise the Cuban government - a plan which became known as Operation Mongoose.

This included a number of bizarre schemes, including one to put powder in Fidel Castro's shoes to make his beard fall out and another which included exploding cigars.

The document suggested that the most effective commander of such an operation would be the then attorney general, the president's brother, Robert Kennedy.

Among those searching for answers in Cuba was the Kennedy's sister, Jean Kennedy Smith.

Battle scene

Walking the beaches of the Bay of Pigs, she said the conference had been a big boost in helping to bring peace between Cuba and the United States.

Another of the US delegates was Alfredo Duran, one of the invading force 40 years ago.

He faced the man he tried to overthrow, Fidel Castro, as well as other Cuban defenders.

As he stood on the beach he said: "This has been a very emotional time, especially discussing with the colonel in charge of the operation the very intense fighting that took place in this spot."

The beaches along the Bay of Pigs in southern Cuba are now littered with sunbeds and overlooked by luxury hotels.

But there is plenty to remind the visitor that this was the scene of an important battle... as the Cubans see it the victory of a small country against an imperialist oppressor.

For the Americans it was a humiliating defeat that helped to shape its Cold War strategy for the next generation and its policy towards Cuba until now.

Kennedy's reluctance

Five kilometres from the beach is a huge poster saying the mercenaries reached this point and all along the road are monuments where the Cuban defenders died.

There are museums at the key battle sites. They chart the story of how almost 2,000 Cuban exiles, trained in Central America by the CIA, tried to invade Cuba in April 1961.

Arthur Schlesinger and Jean Kennedy: Seeking lessons from the defeat

They were hoping the Cuban people would rise up and join them in overthrowing Fidel Castro's Government - or that US troops would follow them on to the beaches.

But the Cuban defence forces destroyed the US support vessels sitting out in the bay and shot down several US planes.

The invaders were left without support and President Kennedy was reluctant to order further help.

After more than two days of fighting several hundred members of the invading force had been killed and more than 1,500 captured.

New understanding

They were held for over a year, until Washington exchanged them for millions of dollars worth of food and medicine.

There was much talk at the conference of how President Kennedy was reluctant to back the invasion.

Posters remind people that Bay of Pigs was the scene of a Cuban victory

One of his former advisers who came to Havana, Arthur Schlesinger, said the president felt obliged to go ahead since he had inherited the plan from the previous Eisenhower administration.

"I advised against it," said Mr Schlesinger, "But my advice was not heeded."

In the aftermath of the failed invasion, any hopes of reconciliation with the United States died and President Castro moved closer into the Soviet camp.

The tension increased, culminating the following year in the Cuban missile crisis when the Soviet Union tried to station nuclear missiles in Cuba, pointing at the United States.

Relations since between Washington and Cuba are still tense.

But in trying to piece together the reasons for the fighting 40 years ago - and by shaking hands with former enemies - all those at the conference said they hoped they'd gone some way to establishing an understanding between the two countries, which lie just 150km apart.