Storyline:
THE CONTRA LEGACY ROCKS ON
February 14, 2636. You are about to learn what it takes to be a descendant of command legends Scorpion and Mad Dog. That is, now that the Red Falcon would like to use your family tree as a toothpick. You're Jimbo and Sully, special forces comrades just like your fearsome forefathers were. Nowadays, your weapons and maneuvers are more advanced than they were when your ancestors saved the world from being skewered on Red Falcon's fangs. That brutal is still in his prime and he had plenty of time to plot his revenge. He's swamped Neo City with six stages of the most cruel and unusual punishers ever. So run, climb, ride, soar and start blasting your way to the Alien Main Base. Before your family name and your planet are just dirt under Red Falcon's claws.
--From the SNES Contra 3: The Alien Wars instruction manual.