The general rules when you marry a EU citizen are:

You can acquire the nationality of your EU partner according to the immigration rules of your partner's country.

You inheritate from the EU rights of your partner in other EU countries according the European Union treaty.

The EU regulation is such that it is always wrapping the national laws (and can be challanged in the EU tribunal of La Haye) and Countries have the obligation to transfer to their local laws the EU regulations. If for example a British Citizen marries a non-EU national and moves to take residence in the UK, he or she will be treated according to UK immigration Laws. Whereas if she moves to another EU State as an Economic Treaty Citizen, she and partner/spouse will be treated generously under EU Law.
Similare example if a non-EU citizen marries an Estonian in Estonia, he or she doesn't automatically acquire EU rights. For the purposes of immigration he or she would be dealt with under Estonian Immigration Laws.He or she will only acquire EU rights, if his Estonian/EU partner takes advantage of an EU Treaty (eg Freedom of Movement) to move to another EU country for economic purposes.

The bottom line is that the right is not automatic. Even thought he or she may be married to an EU partner the right can only initially be exercised by the EU partner through an Economic Treaty. There and then will he or she has access to the Rights.
 [31-01-2005]