Political map of South American nations 04 March 1867 (Invasion of Paraguay): In early 1866 the Triple Alliance of Brazil, Argentina, and Uruguay (Treaty of the Triple Alliance) defeated the last Paraguayan forces in Argentina, successfully crossing the Paraná River into Paraguay itself in April (Paraguayan War). However, southern Paraguay was well protected by river fortifications and it would take another two years' fighting for the Allies to break through.