England, looking to end a 40-year wait for their second title, meet Paraguay in a Group B match in Frankfurt.
Argentina, champions in 1978 and 1986, launch their campaign for a third triumph against dangerous debutants Ivory Coast in a Group C encounter in Hamburg.
The other match on the second day of the month-long tournament features debutants Trinidad & Tobago against Group B rivals Sweden in Dortmund.
England face Paraguay without Wayne Rooney although the 20-year-old striker's broken foot has now healed. He is expected to return later in the tournament.
Sven-Goran Eriksson's England are fancied to do well in the competition but the coach has urged his side to be ruthless against Paraguay.
England have won their last six matches and head into the game in a positive frame of mind.
CARDOZO OUT
Paraguay are without striker Jose Cardozo, ruled out of the World Cup with a calf injury.
But fellow striker Roque Santa Cruz is confident of starting the game despite being short of full fitness.
Argentina also have high hopes of doing well and coach Jose Pekerman, who has already named his team, has warned his players not to underestimate the Ivorians.
Sweden plan to ruin Trinidad's debut by producing a flying start ahead of seemingly tougher matches against Paraguay and England.
Trinidad suffered a blow on the eve of the match when central defender Marvin Andrews was ruled out with a knee injury.
The World Cup began in spectacular style on Friday when Germany beat Costa Rica 4-2 in the highest-scoring opening match in the competition's history.
Ecuador recorded the first upset with a 2-0 win over Poland in the second Group A match.
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