A neuroscience research center with very high field MRI equipments was opened in November 2006 by the CEA life sciences division. Three MRI systems operating at 3, 7 and 17 T have been already installed. One of the imaging systems will require a 11.75 T magnet with a 900 mm warm bore. The large aperture and high field strength of this magnet provide a substantial engineering challenge compared to the largest MRI systems ever built. This magnet is being developed within an ambitious R&D program, Iseult, whose focus is high field MRI. Traditional MRI magnet design principles are not readily applicable and thus concepts taken from high energy physics or fusion experiments, namely the Tore Supra tokamak magnet system, will be used. The coil will be made of a niobium-titanium conductor cooled by a He II bath at 1.8 K, permanently connected to a cryoplant. Due to its design the magnet will be operated in a non-persistent mode. As the field stability needed for MRI imaging requires a field drift of less than 0.05 ppm/h, it is hardly feasible to directly transpose these requirements in the power supply specification. Two existing solutions developed for other applications have been selected: one using a semi-persistent mode, and the other using a short-circuited superconducting coil in the inner bore. In order to make a decision on experimental basis, an ambitious R&D field stability program has been set-up based on magnet prototypes, high field test facility (Seht, a 44 H and 8 T magnet with a warm bore to 600 mm). We will present development and experimental results of the two stabilization solutions. In conclusion, the stability solution selected for the Iseult magnet is given.