An estimated 100,000 supporters gathered in Mexico City's Zocalo Plaza for Andres Lopez Obrador's "inauguration".
Mr Lopez Obrador, who lost July's presidential election by less than one percentage point, declared himself Mexico's "legitimate" president.
Mr Lopez Obrador has alleged electoral fraud cost him the presidency, despite a recount confirming Felipe Calderon as Mexico's president-elect.
Wearing a presidential sash, Mr Lopez Obrador described the ceremony as the start of a "new republic against a neo-fascist oligarchy".
The alternative ceremony took place 11 days before Mr Calderon's official swearing-in as Mexico's president.
Mr Lopez Obrador presented members of his "alternative cabinet" in the "parallel government".
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