"Galaxy Angel" is a dating sim created by BROCCOLI and later adapted as an anime TV series.
Galaxy Angel is a bishoujo dating sim created by BROCCOLI and later adapted as an anime TV series directed by Morio Asaka, Yoshimitsu Ōhashi (first 2 seasons) and Shigehito Takayanagi (last 2 seasons), and produced by Studio Madhouse. The show follows 5 girls (the "Angel Brigade", an elite branch of the military) who search for pieces of Lost Technology, ancient mysterious items with unknown powers.
The first season of the anime, containing 24 episode plus 2 extras, aired in April 2001, shortly followed by an 8 volume manga series written by BROCCOLI. An 18 episode plus 1 extra second season called Galaxy Angel Z aired in February 2002. A 3rd season, split into 3 sections called Galaxy Angel A, Galaxy Angel AA and Galaxy Angel S started airing in November 2002 and contained a total of 53 episodes plus one extra episode. Finally, a 26 episode Galaxy Angel X aired in July 2004. Most of these episodes were roughly 13 minutes in length, and thus were broadcast in pairs in order to fill up a half hour time-slot.
For more information, see the Wikipedia page or the Galaxy Angel wikia.