Bad Dudes:
The game starts in Washington, D.C., where President Ronnie (based on the U.S. President Ronald Reagan) has been abducted by the evil Dragon Ninja. The game's intro begins with the following introduction: "Rampant ninja related crimes these days ... Whitehouse is not the exception". A Secret Service agent speaks to the titular "Bad Dudes", two street-smart brawlers named Blade and Striker: "President Ronnie has been kidnapped by the ninjas. Are you a bad enough dude to rescue Ronnie?" The Bad Dudes pursue the Dragon Ninja through the New York City streets, onto a moving big rig truck, through a large storm sewer, through a forest, onto a freight train on an old Southern Pacific line (where the titular character of another Data East arcade game, Chelnov, can be seen being transported in a frozen container in the arcade version), through a cave, and into an underground factory in order to save President Ronnie.

Two Crude Dudes:
In 2010, an atomic explosion of unknown origin takes place in New York. Twenty years later, just as the rebuilding process is taking place, a criminal organization named "Big Valley" marches into the ruins and takes control. In response to this, the government tasks two men, known under the collective name of "Crude Buster", with secretly entering the ruins in order to regain control by defeating Big Valley, with the promise of a very big cash reward.