Originally Posted by SATCHMO

You're not actually looking for a particular genre of music, if what you're looking for is the use of this musical device, which one might call looped counterpoint, or a fugue. The style that you are describing would definitely fall into minimalism which is a genre that encompasses many different styles, including electronic, orchestral, new age and others, but minimalism isn't strictly defined by the use of that device.

Steve Reich is a post modern classical composer, and while he did a significant amount of work with tape loops and other electronic compositions he also did a lot organic instrumental music that produced the same contrapuntal effect your aiming for, the best example being Music for 18 Musicians. It's definitely worth checking out.