The Delian League was not the only alliance in Greece. After the Persian Wars, many cities in Southern Greece, including Sparta banded together as well. This alliance was called the Peloponnesian League after the peninsula on which the cities were located.
The growth of Athenian power worried many cities in the Peloponesian League. Finally to stop Athen's growth, Sparta declared war.
This declaration war began the Peloponnesian War, a war between Athens and Sparta that threatened to tear all of Greece apart. In 431 BC he Spartan army marched north to Athens. They surrounded the city, waiting for the Athenians to come out and fight. But the Athenians stayed in the city, hoping that the Spartans would leave. Instead the Spartans began to burn he crops in the fields around Athens. They hoped that Athens would run out of food and be ford to surrender.
The Spartans were in for a surprise. The Athenan Navy escorted merchant ships to Athens, bringing food to the city. The navy also attacked Spartans allies, forcing the Spartans to send troops to defend the Greek cities at the same time, though, disease swept through Athens killing thousands. For 10 years neither side could gain an advantage over the other. Eventually, they agreed to a truce Athens kept its empire, and the Spartans went home.