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The capture of Las Villas is a key goal for the rebel force, known as the 26 July Army, before they advance on the capital, Havana.
Despite being heavily outnumbered by the Cuban army, the rebels have enormous popular support and have won a number of significant victories.
Just a few weeks ago, they were confined to their tiny mountain stronghold at the other end of the island. Now they have advanced into a position where they are poised to take the capital itself.
Call for truce
The guerrillas have been fighting to overthrow the military government of Fulgeneio Batista for two years.
But in the last 48 hours about 3,000 people have been killed or injured in some of the bloodiest fighting in the history of Cuba.
The army has countered the rebel attack on Santa Clara with fighter and bomber aircraft, as well as guns and tanks.
One of the rebel leaders, Dr Ernesto "Che" Guevara, has appealed to the government commander in Santa Clara for a truce to clear the streets of the casualties.
Broadcasts on rebel radio said his appeal had been rejected.
The president is reported to be preparing to take personal command of his forces to destroy a convoy of guerrilla soldiers currently moving south from Santa Clara.
In a sign of how desperate the situation has become for the government, President Batista today removed the Commodore of the Navy's air force, Joaquin Yarela Canosa, from his post.
He was the second senior figure in the armed forces to be sacked this week. The army commander in Las Villas, General Alberto Rio Chaviano, lost his job a few days ago.
Meanwhile, amid rumours that President Batista is preparing to flee the island, two of his young sons arrived in New York, accompanied by their grandfather, Manuel Perez Benitoa.
Mr Benitoa denied that the two boys were being evacuated ahead of a government surrender, saying, "I bring them every year to see the snow."
Two days later, on New Year's Day 1959, President Batista fled the country to the Dominican Republic, his government overthrown and his regime at an end.
He was to live the rest of his life in exile in Portugal and Spain and died in Spain in 1973.
Fidel Castro was sworn in as premier on 16 February 1959.
Since then, Cuba has been a one-party state in which Fidel Castro exerts control over virtually every aspect of Cuban life.
From an early stage, his leadership put Cuba on a collision course with the United States.
Antagonism between the two nations led to economic sanctions against Cuba from 1960. Two years later, Fidel Castro brought the world to the brink of nuclear war as his alliance with the USSR provoked the Cuban missile crisis.
Diplomatic relations have never been restored, and the US continues to enforce trade sanctions against Fidel Castro's regime.
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