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What modern scholars call the First Triumvirate was an informal political alliance of two rival generals, Julius Caesar and Pompey the Great representing the popular viz. senatorial party, with the extremely wealthy businessman Marcus Licinius Crassus. This fell apart after the death of Crassus, and the two other triumvirs fought a civil war, during which Pompey was killed and Caesar established his sole rule as perpetual dictator.
Triumvirate - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Triumvirate)

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In 59 B.C. Julius Caesar, Marcus Crassus, and Pompey formed a triple alliance known as the First Triumvirate. Officially, the First Triumvirate held no governing power, but socially, they were the tri-ruling body of the Republic. This league existed until the death Pompey's wife Julia in 54 B.C. and of Crassus in 53 B.C. After the influence of these two had passed, Caesar and Pompey did not have anything left in common and the relationship that existed between the two crumbled into a battle for control of the Roman Republic.

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