António Costa, who is also the prime minister of Portugal, spoke to reporters just before 11:00 p.m.
In the last local elections in 2013, the Socialists won 150 town halls, one of them in coalition (in Funchal, Madeira, and by 11:00 this evening, the party had won 96 of the 175 polls that had already been announced.
Portugal has 309 town halls.
The leader of the main opposition party, Pedro Passos Coelho, has already congratulated the Socialists on their success.