Lieutenant Kei Katsuragi, a fighter pilot, receives a mission to protect a new untested bomb, the Space/Time oscillation bomb. During the mission the bomb goes off, and it produces a catastrophe. Twenty years later, the Emaan, a group of techno-gypsies find Kei unconscious and take him with them. Kei soon discovers he is in another dimension and that the Emaan aren't human.

Kei learns that the Emaan are the natural inhabitants of this world and that they are at war with the Terram, another race. He also learns that he cannot return home, because this world is surrounded by a dimensional barrier that can't be destroyed. Kei tries to penetrate the barrier with his Bronco 2 fighter plane but he fails and his ruined Bronco crashes to earth. Meanwhile, the Terram launch an attack on the Emaan, who retreat and hide in the woods.

Mimsy, one of the Emaans, finds Kei and brings him back to the others. He discovers that the Emaan fighter planes have an anti gravity control system which makes them easier to pilot. Kei asks the Emaan to fix his Bronco and also modify it to fly like their fighter planes. Meanwhile, the Terram supreme commander puts Olson in charge of recovering Kei from the Emaan.

Kei and Mome, a robot girl, decide to look around while the others are rebuilding his Bronco. They arrive in a Terram villaige, where Kai sees a man driving a jeep. The man says he got it from the Emaan, who were the ones who fixed it. On the way back to the market place, two Terram soldiers show up and try to capture Kei. Kei and Mome manage to escape, and race back to the caravan, where the modified Bronco is ready. What Kei doesn't know is that most of the actuators are not hooked up yet, and thus the Bronco cannot do anything else but fly. They take off and manage to get rid of the Terram soldiers. Later, they land in the village, but the villagers are not pleased thinking they will have problems with the Terram now.

The Emaan are welcomed by the villagers after they offer them some free goods. That night, at dinner, Jaby suggests that they rename the modified Bronco Orguss, after their god of war. Meanwhile, two villagers steal the Orguss. Kei leaves to search for it, and finds it in the woods, alongside two men. The younger one of them, Badei, explains to Kei that he only stole the Orguss to save his girlfriend Ereine, who is being held at a Terram base. Kei reluctantly accepts to help them rescue Ereine. Kei attacks the Terram base and manages to get the job done.

Jaby convinces Shaya to stop the Glomar, their caravan, to search for a valley where he believes they will find grapes, which is his favorite food. They arrive in the valley, where they find some huge grapes and decide to stop to harvest them and take them aboard the Glomar.

Mome, the robot girl, has become infatuated with Kei and always wants to be near him. Kei however doesn't really care about her. The Glomar is over the Atlantic Ocean near Gibraltar, where the Emaan are planning to trade with some of the ships at sea. Kei is asked to help carry some of the boxes. He sees Mimsy, who asks him if he likes Mome. Kei answers that he doesn't, and he asks her if she's taken, because he likes her. Later, Sray, who overheard the discussion, argues with Mimsy and asks her again to marry him. Meanwhile, the Terram fleet approaches Gibraltar and detects the Glomar. Robert puts Henry in charge of dealing with Kei while he attacks the Glomar. Govu gives Kei a hand, and they both manage to defeat the Terram squadron.

Kei and the others discuss possible escape routes for eluding the Terram. The best one seems to be fleeing over mainland France. On the deck, Kei tries to impress Mimsy, but without success. She also tells him she hates it when he's so romantic. The Terram arrive and attack the Glomar. Kei and the others engage, but find themselves outnumbered. However, when the Glomar begins to bombard the enemies, Robert is forced to call off the attack. In the end, Kei and Mimsy are on the deck watching the sunset.

The Glomar is hovering above a battlefield, where they meet some survivors, rebels led by Jann who asks the Emaan to help them overthrow the aristocracy. The Emaan already made a contact with Ann months ago, lending her a powerful weapon called the Hasai Cannon. They didn't expect Ann will use it to suppress the peasants, so they agree to help the rebels overthrow Ann and get the weapon back.

After a game of tennis, Kei and Sray continue to argue over Mimsy, and Kei tells Sray that if Mimsy is his woman, he should try to defend her. The ship is soon attacked by a group of barbarians. Sray remembers what Kei told him and decides to be the one who will protect Mimsy. He does so, but he is wounded by one of the enemies.

The Emaan agree that if Kei would die, all of their problems would be over. Soon the Terram attack, and the Orguss flies out of the Glomar. The Terram squadron manages to shoot the Orguss down quite easily, and watch it fall and shatter on the ground.

The Terram supreme commander gives Athena, one of their best pilots, their newest ship, the Nikick. Her mission is to bring Kei to them, alive. Athena finds and engages Kei in a battle, and they seem to be evenly matched.

In order to increase the jamming field of the Glomar, the Emaan decide to send someone out with another jamming device. Shaya mentions that the person who will do it will most likely be found and killed by the Terram. Sray decides to volunteer for this mission.

The Terram supreme commander gives new orders to his army: Kei, the Tokuiten, as they call him, has to be killed. Otherwise, his actions could ruin their secret project, the D-system. Meanwhile, Olson deserts from the Terram army and joins the Emaan aboard the Glomar.

Olson confronts Kei, explaining to him what the Tokuiten really is, and tells him that he should come with him back to the Terram so that they can undo the mess the world is in. Kei is reluctant to believe Olson, but at the same time he vows to himself that he will do whatever he must to repair the world.

The Galmor finally arrives at the Emaan homeland. There, Kei is captured by members of the Toobu clan who wish to brainwash him. Shaya leaves on a mission to save him.

Sray returns to the Galmor to find Mimsy ill. She is ending her period of fertility, and soon she will no longer be able to have children. The Toobu clan attacks the Galmor when they approach Death Valley.

Shaya meets with her sister, Manisha, to discuss about the Tokuiten. Shaya refuses to give Kei to the Toobu. Meanwhile, Olson approaches the Galmor, but he is attacked by a Terram squadron sent to attack the Emaan.

During their fight, Kei and Athena are sucked through a dimensional warp and find themselves in World War 2 era. There, they are forced to take refuge inside a cave, where they get a chance to know each other a little better.

Olson returns to the Galmor to try and convince Kei to come with him to the Terram, in order to repair the world. Kei refuses, but learns more about Athena. They are soon attacked by both the Terram and by the Toobu clan. Using the Hasai Cannon they manage to escape, but Olson is injured during the fight.

Athena returns, and fights Kei. Olson stops the fight, and tells Athena the truth about her relationship with Kei.

Kei must decide now whether to remain with the Emaan or return to the Terram.

The Terram finally complete their D-system, which will allow them to travel through space and time. Using it, a critical time can be found and a bomb planted which will alter history, causing the world to mend. However, the device does have its dangers; misuse of the device could destroy space and time completely. Meanwhile, back at the Galmor, Kei and Olson fall ill, due to the use of the D-system.

The Mu leader reveals his plan: to create a world ruled by the superior machines. But, to do so they must destroy both the Terram and the Emaan. Meanwhile, Manisha agrees to leave Shaya in charge of the Toobu clan.

The Galmor is under attack by the Terram army. Olson is lured into a canyon by Robert. There, Olson tries to convince Robert to desert the Terram army and help the Emaan, like he did.