Five Cubans convicted in the US of spying for Havana have appealed for a retrial, saying they were found guilty because of anti-Castro bias.
It is the third time the Cuban Five have sought a retrial
The men, known as the Cuban Five, were arrested in 1998 and convicted of charges such as using false identities and conspiracy to commit espionage.
Three were given life terms, the other two 15 and 19 years in jail.
US prosecutors insist the men were found guilty after a "soberly-tried case" that was based on hard evidence.
It is the third time the five - Gerardo Hernandez, Ramon Labanino, Rene Gonzalez, Antonio Guerrero and Fernando Gonzalez - have sought to appeal against their 2001 convictions.
Defence lawyers told the Atlanta appeals court the US government committed several acts of misconduct during the men's trial and their sentences were unduly harsh.
Lawyers said the US had used "[Cuban leader Fidel] Castro's evil to argue for the defendants' criminal guilt", displaying a large photo of Mr Castro in front of the jury at the trial.
Cuba's 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.
The year before they were arrested there had been a bombing campaign against tourist sites in Havana. An Italian national was killed and several Cubans injured.
US prosecutors said in court documents that the men's trial was conducted based on hard evidence, "with great care and professionalism".
"This was a soberly tried case. It was squarely based on evidence ... The government did not exploit red-baiting in this case," government lawyer Caroline Heck Miller told the court.
Crowds lined the streets outside the courtroom to watch proceedings.
The men are considered national heroes in Cuba - they figure prominently on billboards all over the country and are the subject of regular rallies and demonstrations, says the BBC's Michael Voss in Havana.
The president of Cuba's National Assembly, Ricardo Alarcon, who is leading an international campaign to secure a retrial, told BBC News the US is applying double standards in the fight against terror.
He said an Iraqi agent allegedly caught spying on anti-Saddam groups in Chicago was jailed for less than four years, "while our people... were considered a danger to the US".
The verdict was initially ruled unsound because it was believed the men could not have received a fair trial in Miami, which has a large Cuban exile community. That ruling was later overturned.