What country were the two “gulf wars” fought against?

The country was Iraq. While the ostensible reason for the invasions of Iraq was to topple a dictator in the name of Saddam Hussein the real reason was because his government had an independent foreign policy ie was not just subservient to US interests in the Middle East plus also for its large reserves of petroleum. In fact, the US government was a friend of Saddam Hussein during his war with Iran previously and helped supply him with arms for this war and accepted his form of government then. 

He droped it over the bridge into the river