So... is Ai no Kusabi finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: May 01, 1994
Manga finished: October 01, 1987
... But MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Ai no Kusabi takes place on the planet Amoi, a stratified society rigidly divided by hair color.
Blond-haired elites, known as Blondies, rule from the advanced city of Tanagura, controlled by the AI Jupiter.
Darker-haired "mongrels" are relegated to the slums of Midas and Ceres.
The story centers on Riki, a former gang leader from Ceres, whose life drastically changes after an encounter with Iason Mink, a powerful Blondie.
Riki is taken to Tanagura and becomes Iason's "pet," experiencing hardship and humiliation.
Upon his return to Ceres, Riki finds himself in a dangerous situation as he navigates the complex power dynamics and struggles for survival, with old alliances forming anew.