Ok this is my attempt, if I understand correctly that Beugegang is the same as Hankenbeugung ("Später, beim ausgebildeten Pferd, müssen sie auch anstrengende Haltearbeit im Beugegang (Hankenbeugung) leisten. http://www.spin.de/forum/msg-archive/208/2008/07/32744"...

engagement of haunches:
"In order for a horse to carry itself gracefully and most efficiently, it must be permitted to carry itself in a posture that allows for balance to improve. The rider must tactfully help the horse find the posture where the haunches are best able to help lift and carry the mass of the rider and the forehand. As the horse engages (lowers and takes weight) onto its haunches it must be free to bring its poll to the highest point and its nose slightly in front of the vertical. The horse uses this position to help distribute the weight rearward." http://www.ridingart.com/balance.htm

"Engagement: Increased flexion of the joints of the hind legs during the WEIGHT BEARING phase, and the sacro-lumbar joint, thus lowering the croup relative to the forehand. A prerequisite for thrust/impulsion." http://www.sustainabledressage.net/collection/true_collectio...

However, I also think that Beugegang could be a combination of engagement of the haunches and collection, in which case a suggestion for the translation would be just that ("engagement of the haunches and collection"). Those concepts (and more, like impulsion) seem to play roles in achieving the Beugegang.

There doesn't seem to be a one-term translation in English, or at least I didn't find it and am not horsey enough to know outright...

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Note added at 1 hr (2014-05-19 16:16:58 GMT)
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Here a definition for collection:
http://horses.about.com/od/glossaryofhorsetermsc/g/collectio...

There seems to be a big discussion about how collected a horse really is, when it seems to have the haunches engaged. I am not sure if these terms (Versammlung, Beugegang) maybe mean the same?