The Nuclear Workers' Association Moruroa E Tatou in French Polynesia says all former nuclear test site workers should be treated equally.
A court in the French territory has begun hearing eight compensation claims by former nuclear workers.
France tested nuclear weapons in the territory for 30 years until 1996 and in March, the French government passed legislation to allow compensation.
The association's president, Roland Oldham, says former French test site workers have been compensated, and his members want the same.
"We just want to get the truth, we just want to have a compensation according to the French law. We cannot accept that the French people in France have a different treatment from the Polynesian people. So we are waiting for the decision."
Roland Oldham says the court's ruling is expected on June the 25th.