Is spraying peroxide on studs with mold enough?
I've seen peroxide and bleach mixtures used frequently to remove mold on studs.  The Natural Resources Defense Council suggests mixing a 1 in 10 bleach solution to clean. The NRDC might be a little too "green" for some people, but the Environmental Research Laboratory at the University of Arizona also has a great article regarding this.  They suggest a bleach to water ratio of 3/4 cup to 1 gal and a minimum 5 minute contact time before rinsing to inactivate and neutralize the mold. Since hydrogen peroxide and bleach do virtually the same thing, I would say the mold is dead if you allowed enough contact time.

However, my concern is the vapor barrier in your picture.

Concrete is porous and will slowly allow moisture to penetrate.  With the vapor barrier on the interior of the studs it will continually trap moisture in between the barrier and the concrete.  This could be the root cause of your moisture problem which caused the mold in the first place.  If so you may be seeing more mold in the future depending on where you live, etc. For more information the EPA has a great technical document on "When Continuous Water Vapor Barriers Shall Not Be Installed."