Article published on the 2010-01-10 Latest update 2010-01-11 12:13 TU
In both territories voters will decide whether they want more self-rule, while remaining part of France.
If they vote yes, their status will change from that of overseas departments to that of overseas collectivities, like far-away French Polynesia whose local authorities has the right to pass some laws.
The technical details would then be decided by a vote in the French parliament.
An opinion poll published on Thursday in Martinique said that 59 per cent of voters are likely to say no.
The vote was announced by President Nicolas Sarkozy when he visited Matrinique in June. It is a response to strikes and riots in French departments in the Caribbean and the Indian Ocean at the beginning of last year.
They were sparked by high unemployment, which stands at 22 per cent in Martinique and a similar level in Guyana, low wages and rising prices.
Martinique, which is in the Caribbean, produces rum and bananas and is a tourist destination for mainland French people. About 300,000 people are entitled to vote there.
French Guyana is on the South American continent and is best known as the launch site for the Ariane European space rockets. About 67,000 people are on the electoral rolls there.
Martinique regional president Alfred Marie-Jeanne declared that a positive vote would be "with no losses and no risks", pointing out that social security rights and membership of the European Union would be maintained.
But opponents say that people are voting without knowing the form of the law which will decide their fate.
A similar proposal in 2003 was rejected by 50.48 per cent of voters in Martinique.
On the Caribbean island of Guadeloupe thousands demonstrated on Saturday against a rise in fuel prices and for wage rises.
The head of the coalition which led last year's general strike, Elie Domota, claimed that the four centimes price rise, which came into effect on 1 January, is illegal and that the pay hikes agreed after last year's strike have not been paid.