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The only news coming out of Cuba is broadcast by the government-run radio station. All other communications with the island have been cut.
THe first landing is reported to have taken place in the early hours of this morning.
Broadcasts from Cuban government radio appealing for medical help indicate that the raiders have successfully penetrated 25 miles (40km) inland.
They appear to have come ashore on an area of the coast known as the Bahía de Cochinos, or Bay of Pigs, south-east of the capital, Havana.
There is no indication as to the size of the invasion force, but Dr Castro, in a speech on Cuban government radio, said they are supported by aircraft and warships.
"The glorious soldiers of the revolutionary army and the national militia are battling the enemy at all the points where they have landed," he said.
The Cuban military have been on high alert for an imminent invasion for some days.
In a speech yesterday, Fidel Castro told the Cuban people he intended to resist such an attack with "an iron hand".
Cuban exiles based in the United States, who are organising the attempt to overthrow the Castro regime, say thousands of Cubans have joined the rebel forces.
However, there is no independent confirmation of the level of support for the invasion from within Cuba.
The leader of the Cuban exile movement in the US, Dr Miro Cardona, said the battle had begun "to liberate our homeland from the despotic rule of Fidel Castro".
Dr Cardona played a part in Fidel Castro's revolution against the dictatorship of President Batista in 1959, and was prime minister for 45 days before Dr Castro himself took over.
In a statement in Washington, the US Secretary of State, Dean Rusk, has again denied US involvement in the invasion of Cuba.
He said the United States had not, and would not intervene in Cuba, with armed forces or otherwise.
Strong suspicions that the United States is sponsoring an offensive against the Castro government have been fuelled by the bombing of three of Cuba's military air bases two days ago.
The US denied all knowledge of the episode, saying Cuban Air Force pilots defecting to Florida were responsible.
But reporters who watched one of the planes land in Miami after carrying out the attack described features which indicated it was American-made.
The invasion of Cuba was carried out by a force of about 1,400 exiled Cubans, with American support from the sea and air.
The main landing point at the Bay of Pigs was a beach surrounded by a mosquito-infested swamp.
The only way to get further in to the island was along just three heavily-defended roads.
The fighting lasted just three days. The invasion force was badly outnumbered and the mass defection of Cubans they had hoped for - their only realistic hope of success - never materialised.
More than 100 of the invasion force died in the attack, and 1,189 were taken prisoner.
Shortly afterwards, President Kennedy acknowledged US support for the invaders.
It was the worst foreign policy embarrassment of his career.
The Bay of Pigs debacle not only strengthened Fidel Castro's hold on power, but also brought the Soviet Union firmly on to his side.
It acted as a key catalyst for the Cuban missile crisis 18 months later, on 28 October 1962, which brought the world to the brink of nuclear war.
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