The Ehlers-Danlos Society has published an article on the many benefits the Alexander Technique offer people with Ehlers-Danlos syndromes (which include hypermobility).
The Alexander Technique regards the body as an inherently connected structure. Through alignment and the prevention of downward pulling tension it reduces pressure on our joints and spine (which is important to people with EDS). The Alexander Technique also helps to avoid hyper extension, facilitates good posture and provides the kind of toning up of the musculature which help to support the joints.
Read the article at the Ehlers-Danlos Society website.