The year is 2065. The world is at war. The two superpowers clash over the space elevator. Far more dangerous than atomic, biological, or chemical weapons are dimensional weapons, such as the Space/Time Oscillation Bomb. Despite the tremendous power of this bomb, it must be armed on-site by a team of engineers.
Desperately, the Freedom Space Corps launch an offensive to plant a Space/Time Oscillation Bomb and destroy the space elevator. During this attack, the engineers are forced to abort the mission and destroy the bomb before it can be properly armed. Enraged at the decision to abort and feeling that his comrades have died in vain, brash fighter pilot Kei Katsuragi haphazardly arms the bomb with severe repercussions.
The explosion transports Kei and his Bronco 2 variable fighter to another world. There he is pursued for unknown reasons by the militaristic Chilam and aided by the Gypsie-like Emaan. Both sides have some unknown interest in Kei referring to him as a "Tokuiten" (特異点?, lit. "singular point"). Originally translated by Tokyo Movie Shinsha as "Differentiated Idioblast", it is more properly translated as "Singularity". In the ImaginAsian version, it's been translated as an "Idiosyncratic Point".
After Kei's fighter is damaged during a fight the Emaan modify it into the Orguss, the titular mecha from the series.