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It is no problem for foreigners to acquire property in Portugal. The registration system and the notary service are well established but it is important to have a property thoroughly checked before buying anything.
Until the revolution of 1974, many Madeirans did not attend school; therefore real estate was quite often not properly registered with the authorities but handed down in the family based on old customs. Furthermore, many inhabitants emigrated in the 1930 – 1940´s. As the families are still large, a nice property may have a legally muddled situation, with many heirs living far away. Such a house might be beautiful and enticing but almost impossible to buy.
Luckily, there are many nice houses and apartments at good prices on the market, and the price level is lower than in the Canary Islands or the Algarve.
Spoiled for choice…