Final answer:
Athens and Sparta fought the Peloponnesian War from 431-404 BCE, which ended with Athens' defeat and a truce. The loss of the Athenian fleet in 405 BCE was decisive, leading to Sparta's temporary dominance until Theban victories challenged Spartan power after 371 BCE. Both city-states' influence declined due to continual warfare.
Step-by-step explanation:
Peloponnesian War Duration and Truce
The Athenians and Spartans fought a protracted conflict known as the Peloponnesian War, which stretched from 431-404 BCE before both city-states were greatly weakened and agreed to a truce. The war could be characterized by several phases, with a brief respite with the Peace of Nicias in 421 BCE, which lasted only until 415 BCE when conflict resumed. The Athenian military suffered a catastrophic defeat in Syracuse. Coupled with internal strife, a devastating plague, and continuous military pressure from Sparta, Athens eventually had to sue for peace after the loss of their fleet in 405 BCE. Sparta, with the help of Persian allies, emerged as the dominant force, imposing a series of oligarchic governments in former Athenian territories.
Sparta, however, did not enjoy its supremacy for long. The rise of Thebes and their victory at the Battle of Leuctra in 371 BCE, followed by campaigns that liberated regions under Spartan control and challenged Spartan hegemony, marked the decline of Sparta as well. These conflicts, coupled with economic and political exhaustion, eventually led to a significant reduction in the influence of both Athens and Sparta.