The five men were arrested in the US in 1998
The US Supreme Court has refused to review the case of five Cubans who are serving long sentences in the US for spying for the Castro government.
The men, convicted in 2001, argue that they did not get a fair hearing at the original trial in Miami because of anti-Castro sentiment in the city.
But the Supreme Court justices, without elaborating, refused to hear an appeal.
In Cuba, where the men are regarded as heroes, the authorities denounced what they called "a monstrous injustice".
The men, Gerardo Hernandez, Ramon Labanino, Antonio Guerrero, Fernando Gonzalez and Rene Gonzalez, were found guilty of infiltrating US military bases and Cuban exile groups, and giving the information to Cuba.
Hernandez was also convicted of conspiracy to commit murder over the shooting-down in 1996 of two planes flown by a Cuban exile group, Brothers to the Rescue.
The five, who received terms ranging from 15 years to life, have made several appeals against their convictions and sentences.
They say that by being tried in Miami, the centre of anti-Castro Cuban exiles, they were victims of bias.
US prosecutors have insisted the men were found guilty on hard evidence, while Cuban exile groups say they were justly punished.
Last year, an appeals court upheld their convictions but ordered three of the men to be resentenced.
The men are considered national heroes in Cuba, where they figure prominently on billboards all over the country and are the subject of regular rallies and demonstrations.
A statement by the Cuban National Assembly said the Supreme Court's decision showed the arbitrary and corrupt nature of American justice and that the judges had acted on the orders of President Barack Obama.
The Cuban government says the men were not in Miami to spy on the US but to prevent anti-Castro exile groups from launching what it calls terrorist attacks on Cuba.